SOLUTION: Suppose f'(x)=-2x and g'(x)=x^2 and g(4)=-1/4. find the derivative of f(g(4)).

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Suppose f'(x)=-2x and g'(x)=x^2 and g(4)=-1/4. find the derivative of f(g(4)).      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1026695: Suppose f'(x)=-2x and g'(x)=x^2 and g(4)=-1/4. find the derivative of f(g(4)).
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
g'(x) = x%5E2 ==> g%28x%29+=+x%5E3%2F3+%2B+c for some constant c.
g(4) = -1/4 ==> g%284%29+=+4%5E3%2F3+%2Bc+=+-1%2F4 ==> c = -259/12.
==> g%28x%29+=+x%5E3%2F3+-+259%2F12
Now f'(x) = -2x ==> f%28x%29+=+-x%5E2+%2B+k for some constant k.
==> f%28g%28x%29%29+=+-%28x%5E3%2F3+-+259%2F12%29%5E2+%2B+k
==> df%28g%28x%29%29%2Fdx+=+-2x%5E2%28x%5E3%2F3+-+259%2F12%29
==> df%28g%284%29%29%2Fdx+=+-2%2A4%5E2%284%5E3%2F3+-+259%2F12%29+=+8