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Is this work right?...

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Is this work right?...

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Dick

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Looks fine to me!First a table is given (im gunna try to reconstruct it; the dashes represent spaces)

X---U(x)---V(x)---U'(x)----V'(x)

2----3--------4------(-1)-------2

3----2--------1--------3------(-1)

4----1--------3--------0-------(-2)

U(x) and V(x) are defined and differentiable for all real numbers x. the following data is known about U,V, and their derivatives.

Define f(x)=[U(x)]^{3}+2[v(x)]^{2}

Find f '(2)

_________________________________________________________________

I was able to use the chain rule to simply it. And so far I gotMy work below

f '(x)=3[U(x)]^{2}(U'(x)) + 4[V(x)][V'(x)]

This is where I'm not really to sure what to do.

I'm thinking you plug in the values from the table in here but I think I might be putting in the wrong values. Do I only use the values at x=2 because its asking for f '(2)?

f '(2)=3[3]^{2}(-1) + 4[4](2)

f '(2)= -27+32

f '(2)=5

Is this work right?

- #3

Mark44

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Yes.First a table is given (im gunna try to reconstruct it; the dashes represent spaces)

X---U(x)---V(x)---U'(x)----V'(x)

2----3--------4------(-1)-------2

3----2--------1--------3------(-1)

4----1--------3--------0-------(-2)

U(x) and V(x) are defined and differentiable for all real numbers x. the following data is known about U,V, and their derivatives.

Define f(x)=[U(x)]^{3}+2[v(x)]^{2}

Find f '(2)

_________________________________________________________________

I was able to use the chain rule to simply it. And so far I gotMy work below

f '(x)=3[U(x)]^{2}(U'(x)) + 4[V(x)][V'(x)]

This is where I'm not really to sure what to do.

I'm thinking you plug in the values from the table in here but I think I might be putting in the wrong values. Do I only use the values at x=2 because its asking for f '(2)?

Yes. Good job!f '(2)=3[3]^{2}(-1) + 4[4](2)

f '(2)= -27+32

f '(2)=5

Is this work right?

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So for example if it said f '(3) I would only use the x values at 3 which are [2,1,3,-1]?

- #5

Ray Vickson

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What do _you_ think? You know the answer; you just need to be more confident.

So for example if it said f '(3) I would only use the x values at 3 which are [2,1,3,-1]?

RGV

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