The range of $ab$ if $|a| le 1$ and $a + b = 1$, $a,binmathbb R$? [closed]
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The range of $ab$ if $|a| le 1$ and $a + b = 1$, $a,binmathbb R$ ?
inequality
edited Nov 20 at 4:29
Jimmy R.
33k42157
asked Nov 20 at 4:23
Alvin Carter
13
closed as off-topic by Jimmy R., Hans Lundmark, KReiser, José Carlos Santos, Christopher Nov 20 at 13:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jimmy R., Hans Lundmark, KReiser, José Carlos Santos, Christopher
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
-2
down vote
favorite
The range of $ab$ if $|a| le 1$ and $a + b = 1$, $a,binmathbb R$ ?
inequality
edited Nov 20 at 4:29
Jimmy R.
33k42157
asked Nov 20 at 4:23
Alvin Carter
13
closed as off-topic by Jimmy R., Hans Lundmark, KReiser, José Carlos Santos, Christopher Nov 20 at 13:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jimmy R., Hans Lundmark, KReiser, José Carlos Santos, Christopher
If this question can be reworded to fit the rules in the help center, please edit the question.
1
What are your attempts?
– Aniruddha Deshmukh
Nov 20 at 4:27
Used AM GM inequality , got max value Right , which is 1/4. But minimum ??
– Alvin Carter
Nov 20 at 5:29
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
The range of $ab$ if $|a| le 1$ and $a + b = 1$, $a,binmathbb R$ ?
inequality
edited Nov 20 at 4:29
Jimmy R.
33k42157
asked Nov 20 at 4:23
Alvin Carter
13
The range of $ab$ if $|a| le 1$ and $a + b = 1$, $a,binmathbb R$ ?
inequality
inequality
edited Nov 20 at 4:29
Jimmy R.
33k42157
asked Nov 20 at 4:23
Alvin Carter
13
edited Nov 20 at 4:29
Jimmy R.
33k42157
asked Nov 20 at 4:23
Alvin Carter
13
edited Nov 20 at 4:29
Jimmy R.
33k42157
edited Nov 20 at 4:29
Jimmy R.
33k42157
edited Nov 20 at 4:29
Jimmy R.
33k42157
33k42157
asked Nov 20 at 4:23
Alvin Carter
13
asked Nov 20 at 4:23
Alvin Carter
13
asked Nov 20 at 4:23
Alvin Carter
13
13
closed as off-topic by Jimmy R., Hans Lundmark, KReiser, José Carlos Santos, Christopher Nov 20 at 13:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jimmy R., Hans Lundmark, KReiser, José Carlos Santos, Christopher
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Jimmy R., Hans Lundmark, KReiser, José Carlos Santos, Christopher Nov 20 at 13:25
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jimmy R., Hans Lundmark, KReiser, José Carlos Santos, Christopher
If this question can be reworded to fit the rules in the help center, please edit the question.
1
What are your attempts?
– Aniruddha Deshmukh
Nov 20 at 4:27
Used AM GM inequality , got max value Right , which is 1/4. But minimum ??
– Alvin Carter
Nov 20 at 5:29
add a comment |
1
What are your attempts?
– Aniruddha Deshmukh
Nov 20 at 4:27
Used AM GM inequality , got max value Right , which is 1/4. But minimum ??
– Alvin Carter
Nov 20 at 5:29
1
1
What are your attempts?
– Aniruddha Deshmukh
Nov 20 at 4:27
What are your attempts?
– Aniruddha Deshmukh
Nov 20 at 4:27
Used AM GM inequality , got max value Right , which is 1/4. But minimum ??
– Alvin Carter
Nov 20 at 5:29
Used AM GM inequality , got max value Right , which is 1/4. But minimum ??
– Alvin Carter
Nov 20 at 5:29
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Hint: $|a|ge 1$ implies that $-1le ale 1$. Also, $a+b=1$ implies that $b=1-a$, hence $$ab=a(1-a)$$
So, your task is to find the minimum and the maximum of the function $f(a)=a(1-a)$ in the interval $ain [-1,1]$. Can you do it?
answered Nov 20 at 4:28
Jimmy R.
33k42157
Got minimum value 1/4. But Maximum ?? By plotting graph its easy, but is there any mathematical method ??
– Alvin Carter
Nov 20 at 5:35
@AlvinCarter Have you been taught derivatives?
– Jimmy R.
Nov 20 at 5:58
Ya. I did it with both by AM-GM inequality as well as derivative equating to zero. But, it giving me the maximum value. How can I find minimum ?
– Alvin Carter
Nov 20 at 6:13
Did you check the value of the function at the edges of the acceptable domain? Does this ring a bell?
– Jimmy R.
Nov 20 at 6:45
1
Oh... Now I got it. At one of the edge , the Minimum is -2. Thanks ! Cheers.
– Alvin Carter
Nov 20 at 8:21
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Hint: $|a|ge 1$ implies that $-1le ale 1$. Also, $a+b=1$ implies that $b=1-a$, hence $$ab=a(1-a)$$
So, your task is to find the minimum and the maximum of the function $f(a)=a(1-a)$ in the interval $ain [-1,1]$. Can you do it?
answered Nov 20 at 4:28
Jimmy R.
33k42157
Got minimum value 1/4. But Maximum ?? By plotting graph its easy, but is there any mathematical method ??
– Alvin Carter
Nov 20 at 5:35
@AlvinCarter Have you been taught derivatives?
– Jimmy R.
Nov 20 at 5:58
Ya. I did it with both by AM-GM inequality as well as derivative equating to zero. But, it giving me the maximum value. How can I find minimum ?
– Alvin Carter
Nov 20 at 6:13
Did you check the value of the function at the edges of the acceptable domain? Does this ring a bell?
– Jimmy R.
Nov 20 at 6:45
1
Oh... Now I got it. At one of the edge , the Minimum is -2. Thanks ! Cheers.
– Alvin Carter
Nov 20 at 8:21
add a comment |
up vote
1
down vote
accepted
Hint: $|a|ge 1$ implies that $-1le ale 1$. Also, $a+b=1$ implies that $b=1-a$, hence $$ab=a(1-a)$$
So, your task is to find the minimum and the maximum of the function $f(a)=a(1-a)$ in the interval $ain [-1,1]$. Can you do it?
answered Nov 20 at 4:28
Jimmy R.
33k42157
Got minimum value 1/4. But Maximum ?? By plotting graph its easy, but is there any mathematical method ??
– Alvin Carter
Nov 20 at 5:35
@AlvinCarter Have you been taught derivatives?
– Jimmy R.
Nov 20 at 5:58
Ya. I did it with both by AM-GM inequality as well as derivative equating to zero. But, it giving me the maximum value. How can I find minimum ?
– Alvin Carter
Nov 20 at 6:13
Did you check the value of the function at the edges of the acceptable domain? Does this ring a bell?
– Jimmy R.
Nov 20 at 6:45
1
Oh... Now I got it. At one of the edge , the Minimum is -2. Thanks ! Cheers.
– Alvin Carter
Nov 20 at 8:21
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Hint: $|a|ge 1$ implies that $-1le ale 1$. Also, $a+b=1$ implies that $b=1-a$, hence $$ab=a(1-a)$$
So, your task is to find the minimum and the maximum of the function $f(a)=a(1-a)$ in the interval $ain [-1,1]$. Can you do it?
answered Nov 20 at 4:28
Jimmy R.
33k42157
Hint: $|a|ge 1$ implies that $-1le ale 1$. Also, $a+b=1$ implies that $b=1-a$, hence $$ab=a(1-a)$$
So, your task is to find the minimum and the maximum of the function $f(a)=a(1-a)$ in the interval $ain [-1,1]$. Can you do it?
answered Nov 20 at 4:28
Jimmy R.
33k42157
answered Nov 20 at 4:28
Jimmy R.
33k42157
answered Nov 20 at 4:28
Jimmy R.
33k42157
answered Nov 20 at 4:28
Jimmy R.
33k42157
33k42157
Got minimum value 1/4. But Maximum ?? By plotting graph its easy, but is there any mathematical method ??
– Alvin Carter
Nov 20 at 5:35
@AlvinCarter Have you been taught derivatives?
– Jimmy R.
Nov 20 at 5:58
Ya. I did it with both by AM-GM inequality as well as derivative equating to zero. But, it giving me the maximum value. How can I find minimum ?
– Alvin Carter
Nov 20 at 6:13
Did you check the value of the function at the edges of the acceptable domain? Does this ring a bell?
– Jimmy R.
Nov 20 at 6:45
1
Oh... Now I got it. At one of the edge , the Minimum is -2. Thanks ! Cheers.
– Alvin Carter
Nov 20 at 8:21
add a comment |
Got minimum value 1/4. But Maximum ?? By plotting graph its easy, but is there any mathematical method ??
– Alvin Carter
Nov 20 at 5:35
@AlvinCarter Have you been taught derivatives?
– Jimmy R.
Nov 20 at 5:58
Ya. I did it with both by AM-GM inequality as well as derivative equating to zero. But, it giving me the maximum value. How can I find minimum ?
– Alvin Carter
Nov 20 at 6:13
Did you check the value of the function at the edges of the acceptable domain? Does this ring a bell?
– Jimmy R.
Nov 20 at 6:45
1
Oh... Now I got it. At one of the edge , the Minimum is -2. Thanks ! Cheers.
– Alvin Carter
Nov 20 at 8:21
Got minimum value 1/4. But Maximum ?? By plotting graph its easy, but is there any mathematical method ??
– Alvin Carter
Nov 20 at 5:35
Got minimum value 1/4. But Maximum ?? By plotting graph its easy, but is there any mathematical method ??
– Alvin Carter
Nov 20 at 5:35
@AlvinCarter Have you been taught derivatives?
– Jimmy R.
Nov 20 at 5:58
@AlvinCarter Have you been taught derivatives?
– Jimmy R.
Nov 20 at 5:58
Ya. I did it with both by AM-GM inequality as well as derivative equating to zero. But, it giving me the maximum value. How can I find minimum ?
– Alvin Carter
Nov 20 at 6:13
Ya. I did it with both by AM-GM inequality as well as derivative equating to zero. But, it giving me the maximum value. How can I find minimum ?
– Alvin Carter
Nov 20 at 6:13
Did you check the value of the function at the edges of the acceptable domain? Does this ring a bell?
– Jimmy R.
Nov 20 at 6:45
Did you check the value of the function at the edges of the acceptable domain? Does this ring a bell?
– Jimmy R.
Nov 20 at 6:45
1
1
Oh... Now I got it. At one of the edge , the Minimum is -2. Thanks ! Cheers.
– Alvin Carter
Nov 20 at 8:21
Oh... Now I got it. At one of the edge , the Minimum is -2. Thanks ! Cheers.
– Alvin Carter
Nov 20 at 8:21
add a comment |
1
What are your attempts?
– Aniruddha Deshmukh
Nov 20 at 4:27
Used AM GM inequality , got max value Right , which is 1/4. But minimum ??
– Alvin Carter
Nov 20 at 5:29