amy0799
  • amy0799
Consider the following function.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amy0799
  • amy0799
\[f(x)=\frac{ 3 }{ x^2 }\] Find the equation of the tangent line T to the graph of f at the point (2,0.75). T(x) =
SolomonZelman
  • SolomonZelman
This is a calculus question, right?
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle f'(x)=~? }\)

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amy0799
  • amy0799
Use this linear approximation to complete the table below. (Give your answer correct to 2 decimal places.) |dw:1446407804716:dw|
amy0799
  • amy0799
yes it's a calculus question
SolomonZelman
  • SolomonZelman
But we don't know T(x), do we?
SolomonZelman
  • SolomonZelman
We can find f\('\)(2), and that will be the slope of the tangent line. Then, using the slope m=f\('\)(2) (whatever f\('\)(2) will come out to) and your point (2, 0.75), you will be able to get the equation of the line.
amy0799
  • amy0799
f'(2)=-0.75
SolomonZelman
  • SolomonZelman
Yes, that is right
SolomonZelman
  • SolomonZelman
So, you have: Slope: \({\rm m}=-0.75\) Point: \( {\rm P} \left( 2,{~} 0.75\right)\)
amy0799
  • amy0799
y-0.75=-0.75(x-2)
SolomonZelman
  • SolomonZelman
yes, that is exactly correct.
amy0799
  • amy0799
y=-0.75x+2.25 This correct?
SolomonZelman
  • SolomonZelman
Yup
SolomonZelman
  • SolomonZelman
And if you ever want to check, you can graph it on desmos.com
amy0799
  • amy0799
how do i find T(x)?
SolomonZelman
  • SolomonZelman
That is it, that is the equation of the tangent line that you needed:)
SolomonZelman
  • SolomonZelman
or is this not so?
amy0799
  • amy0799
oh so T(x) is the derivative of f(x)?
amy0799
  • amy0799
r u there?
SolomonZelman
  • SolomonZelman
T(x), I think, is the equation of the equation of the tangent line.
amy0799
  • amy0799
what do u mean?
amy0799
  • amy0799
oh wait nvmd i got it
amy0799
  • amy0799
can u help me with another question?
SolomonZelman
  • SolomonZelman
I can try :)
amy0799
  • amy0799
it's a graph but i dont know how to take a screenshot of it
SolomonZelman
  • SolomonZelman
oh well...
amy0799
  • amy0799
ill just draw it the best i can
amy0799
  • amy0799
|dw:1446409485799:dw| Use differentials and the graph of g' to approximate g(2.95) and g(3.1) given that g(3) = 3 g(2.95) ≈ g(3.1) ≈
SolomonZelman
  • SolomonZelman
is this it?
amy0799
  • amy0799
yes
SolomonZelman
  • SolomonZelman
You are given that g(3)=3, and g'(3)=3. Am I right?
SolomonZelman
  • SolomonZelman
That means you can extract the equation of the tangent line at x=3. y-3=3(x-3) ---> y=3x-6 Lets call this tangent line S(x). So, S(x)=3x-6 And use that to approximate g(2.95), and g(3.1). This would mean that: g(2.95) ≈ S(2.95) g(3.1) ≈ S(3.1)
SolomonZelman
  • SolomonZelman
Hope this helps.

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