Let $f(x) = 2x^2$. Approximate $f(103)$ using tangent line at $x=100$ [closed] Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Tangent line solution at a given set of points?Tangent Line to the curve that is Parallel to the lineVertical Tangent line in Explicit Function question?Tangent of a Straight LineEquation of a Tangent Line Using Trig DerivativesFinding common tangent line to two functionsHow can I use the differencial to approximate a function with a tangent plane?Tangent line problem using differential equationsFinding the approximate error using partial differentiationTangent line, normal line - confusing.
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Let $f(x) = 2x^2$. Approximate $f(103)$ using tangent line at $x=100$ [closed]
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Tangent line solution at a given set of points?Tangent Line to the curve that is Parallel to the lineVertical Tangent line in Explicit Function question?Tangent of a Straight LineEquation of a Tangent Line Using Trig DerivativesFinding common tangent line to two functionsHow can I use the differencial to approximate a function with a tangent plane?Tangent line problem using differential equationsFinding the approximate error using partial differentiationTangent line, normal line - confusing.
$begingroup$
How do I solve it? More interested in learning the process, not the answer! Thank you!
calculus derivatives linear-approximation
edited Apr 1 at 6:50
rash
568216
asked Apr 1 at 6:35
Aman KhanAman Khan
326
$endgroup$
closed as off-topic by Eevee Trainer, José Carlos Santos, Xander Henderson, Shailesh, YiFan Apr 2 at 0:44
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, José Carlos Santos, Xander Henderson, Shailesh, YiFan
add a comment |
$begingroup$
How do I solve it? More interested in learning the process, not the answer! Thank you!
calculus derivatives linear-approximation
edited Apr 1 at 6:50
rash
568216
asked Apr 1 at 6:35
Aman KhanAman Khan
326
$endgroup$
closed as off-topic by Eevee Trainer, José Carlos Santos, Xander Henderson, Shailesh, YiFan Apr 2 at 0:44
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, José Carlos Santos, Xander Henderson, Shailesh, YiFan
$begingroup$
Compute the tangent line $L(x)$ through $f(100)$, then compute $L(103)$.
$endgroup$
– William
Apr 1 at 13:19
add a comment |
$begingroup$
How do I solve it? More interested in learning the process, not the answer! Thank you!
calculus derivatives linear-approximation
edited Apr 1 at 6:50
rash
568216
asked Apr 1 at 6:35
Aman KhanAman Khan
326
$endgroup$
How do I solve it? More interested in learning the process, not the answer! Thank you!
calculus derivatives linear-approximation
calculus derivatives linear-approximation
edited Apr 1 at 6:50
rash
568216
asked Apr 1 at 6:35
Aman KhanAman Khan
326
edited Apr 1 at 6:50
rash
568216
asked Apr 1 at 6:35
Aman KhanAman Khan
326
edited Apr 1 at 6:50
rash
568216
edited Apr 1 at 6:50
rash
568216
edited Apr 1 at 6:50
rash
568216
568216
asked Apr 1 at 6:35
Aman KhanAman Khan
326
asked Apr 1 at 6:35
Aman KhanAman Khan
326
asked Apr 1 at 6:35
Aman KhanAman Khan
326
326
closed as off-topic by Eevee Trainer, José Carlos Santos, Xander Henderson, Shailesh, YiFan Apr 2 at 0:44
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, José Carlos Santos, Xander Henderson, Shailesh, YiFan
closed as off-topic by Eevee Trainer, José Carlos Santos, Xander Henderson, Shailesh, YiFan Apr 2 at 0:44
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, José Carlos Santos, Xander Henderson, Shailesh, YiFan
$begingroup$
Compute the tangent line $L(x)$ through $f(100)$, then compute $L(103)$.
$endgroup$
– William
Apr 1 at 13:19
add a comment |
$begingroup$
Compute the tangent line $L(x)$ through $f(100)$, then compute $L(103)$.
$endgroup$
– William
Apr 1 at 13:19
$begingroup$
Compute the tangent line $L(x)$ through $f(100)$, then compute $L(103)$.
$endgroup$
– William
Apr 1 at 13:19
$begingroup$
Compute the tangent line $L(x)$ through $f(100)$, then compute $L(103)$.
$endgroup$
– William
Apr 1 at 13:19
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Calculate the slope $f’(100)$ of the tangent line. You also know a point if it, namely $(100,f(100))$. Now write down the line’s equation and plug in $103$.
answered Apr 1 at 6:42
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
add a comment |
$begingroup$
I think $f(x+Delta x)-f(x)approx f'(x),Delta x$. And the approximation would be better for smaller $Delta x$.
In this case, you have $f(x)=2x^2$. Take $x=100$ and so $Delta x=3$.
You may then approximate $f(103)approx f(100)+f'(100)cdot 3$.
edited Apr 1 at 6:48
Arthur
123k7122211
answered Apr 1 at 6:44
AdmuthAdmuth
886
$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Calculate the slope $f’(100)$ of the tangent line. You also know a point if it, namely $(100,f(100))$. Now write down the line’s equation and plug in $103$.
answered Apr 1 at 6:42
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
add a comment |
$begingroup$
Calculate the slope $f’(100)$ of the tangent line. You also know a point if it, namely $(100,f(100))$. Now write down the line’s equation and plug in $103$.
answered Apr 1 at 6:42
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
add a comment |
$begingroup$
Calculate the slope $f’(100)$ of the tangent line. You also know a point if it, namely $(100,f(100))$. Now write down the line’s equation and plug in $103$.
answered Apr 1 at 6:42
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
Calculate the slope $f’(100)$ of the tangent line. You also know a point if it, namely $(100,f(100))$. Now write down the line’s equation and plug in $103$.
answered Apr 1 at 6:42
Michael HoppeMichael Hoppe
11.3k31837
answered Apr 1 at 6:42
Michael HoppeMichael Hoppe
11.3k31837
answered Apr 1 at 6:42
Michael HoppeMichael Hoppe
11.3k31837
answered Apr 1 at 6:42
Michael HoppeMichael Hoppe
11.3k31837
11.3k31837
add a comment |
add a comment |
$begingroup$
I think $f(x+Delta x)-f(x)approx f'(x),Delta x$. And the approximation would be better for smaller $Delta x$.
In this case, you have $f(x)=2x^2$. Take $x=100$ and so $Delta x=3$.
You may then approximate $f(103)approx f(100)+f'(100)cdot 3$.
edited Apr 1 at 6:48
Arthur
123k7122211
answered Apr 1 at 6:44
AdmuthAdmuth
886
$endgroup$
add a comment |
$begingroup$
I think $f(x+Delta x)-f(x)approx f'(x),Delta x$. And the approximation would be better for smaller $Delta x$.
In this case, you have $f(x)=2x^2$. Take $x=100$ and so $Delta x=3$.
You may then approximate $f(103)approx f(100)+f'(100)cdot 3$.
edited Apr 1 at 6:48
Arthur
123k7122211
answered Apr 1 at 6:44
AdmuthAdmuth
886
$endgroup$
add a comment |
$begingroup$
I think $f(x+Delta x)-f(x)approx f'(x),Delta x$. And the approximation would be better for smaller $Delta x$.
In this case, you have $f(x)=2x^2$. Take $x=100$ and so $Delta x=3$.
You may then approximate $f(103)approx f(100)+f'(100)cdot 3$.
edited Apr 1 at 6:48
Arthur
123k7122211
answered Apr 1 at 6:44
AdmuthAdmuth
886
$endgroup$
I think $f(x+Delta x)-f(x)approx f'(x),Delta x$. And the approximation would be better for smaller $Delta x$.
In this case, you have $f(x)=2x^2$. Take $x=100$ and so $Delta x=3$.
You may then approximate $f(103)approx f(100)+f'(100)cdot 3$.
edited Apr 1 at 6:48
Arthur
123k7122211
answered Apr 1 at 6:44
AdmuthAdmuth
886
edited Apr 1 at 6:48
Arthur
123k7122211
edited Apr 1 at 6:48
Arthur
123k7122211
edited Apr 1 at 6:48
Arthur
123k7122211
123k7122211
answered Apr 1 at 6:44
AdmuthAdmuth
886
answered Apr 1 at 6:44
AdmuthAdmuth
886
answered Apr 1 at 6:44
AdmuthAdmuth
886
886
add a comment |
add a comment |
$begingroup$
Compute the tangent line $L(x)$ through $f(100)$, then compute $L(103)$.
$endgroup$
– William
Apr 1 at 13:19