Slope, Tangent and Rate of Change
Is “the slope of the tangent to a curve at a point” the same as “the slope of the curve at a point”? Can a single point have a slope or is it only defined for two or more points that form a straight line?
Furthermore is the “slope” of a function the same as the “rate of change” of a function? Because I never see people saying the “slope” of a function but only the “rate of change” of a function which has lead me to believe that “slope” is purely a geometric concept. Correct me if I am wrong. Thanks in advance.
calculus derivatives
asked Nov 26 at 9:46
J. Smith
241
add a comment |
Is “the slope of the tangent to a curve at a point” the same as “the slope of the curve at a point”? Can a single point have a slope or is it only defined for two or more points that form a straight line?
Furthermore is the “slope” of a function the same as the “rate of change” of a function? Because I never see people saying the “slope” of a function but only the “rate of change” of a function which has lead me to believe that “slope” is purely a geometric concept. Correct me if I am wrong. Thanks in advance.
calculus derivatives
asked Nov 26 at 9:46
J. Smith
241
add a comment |
Is “the slope of the tangent to a curve at a point” the same as “the slope of the curve at a point”? Can a single point have a slope or is it only defined for two or more points that form a straight line?
Furthermore is the “slope” of a function the same as the “rate of change” of a function? Because I never see people saying the “slope” of a function but only the “rate of change” of a function which has lead me to believe that “slope” is purely a geometric concept. Correct me if I am wrong. Thanks in advance.
calculus derivatives
asked Nov 26 at 9:46
J. Smith
241
Is “the slope of the tangent to a curve at a point” the same as “the slope of the curve at a point”? Can a single point have a slope or is it only defined for two or more points that form a straight line?
Furthermore is the “slope” of a function the same as the “rate of change” of a function? Because I never see people saying the “slope” of a function but only the “rate of change” of a function which has lead me to believe that “slope” is purely a geometric concept. Correct me if I am wrong. Thanks in advance.
calculus derivatives
calculus derivatives
asked Nov 26 at 9:46
J. Smith
241
asked Nov 26 at 9:46
J. Smith
241
asked Nov 26 at 9:46
J. Smith
241
asked Nov 26 at 9:46
J. Smith
241
asked Nov 26 at 9:46
J. Smith
241
241
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
Yes it is, the slope or gradient of the curve is the same as the slope or gradient of the tangent at that same point, but a single point can not have a slope. Because the slope is the ratio of the difference in y- coordinates and x- coordinates. Secondly, the slope of a function is not the rate of change but rather the gradient function is the same as the rate of change.
answered Nov 26 at 10:02
Bravie
143
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3014112%2fslope-tangent-and-rate-of-change%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Yes it is, the slope or gradient of the curve is the same as the slope or gradient of the tangent at that same point, but a single point can not have a slope. Because the slope is the ratio of the difference in y- coordinates and x- coordinates. Secondly, the slope of a function is not the rate of change but rather the gradient function is the same as the rate of change.
answered Nov 26 at 10:02
Bravie
143
add a comment |
Yes it is, the slope or gradient of the curve is the same as the slope or gradient of the tangent at that same point, but a single point can not have a slope. Because the slope is the ratio of the difference in y- coordinates and x- coordinates. Secondly, the slope of a function is not the rate of change but rather the gradient function is the same as the rate of change.
answered Nov 26 at 10:02
Bravie
143
add a comment |
Yes it is, the slope or gradient of the curve is the same as the slope or gradient of the tangent at that same point, but a single point can not have a slope. Because the slope is the ratio of the difference in y- coordinates and x- coordinates. Secondly, the slope of a function is not the rate of change but rather the gradient function is the same as the rate of change.
answered Nov 26 at 10:02
Bravie
143
Yes it is, the slope or gradient of the curve is the same as the slope or gradient of the tangent at that same point, but a single point can not have a slope. Because the slope is the ratio of the difference in y- coordinates and x- coordinates. Secondly, the slope of a function is not the rate of change but rather the gradient function is the same as the rate of change.
answered Nov 26 at 10:02
Bravie
143
answered Nov 26 at 10:02
Bravie
143
answered Nov 26 at 10:02
Bravie
143
answered Nov 26 at 10:02
Bravie
143
143
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3014112%2fslope-tangent-and-rate-of-change%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
