3 years ago
The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(J(x)).
Find each derivative , if it exists. If the derivative ve does not exist, explain why.
Find s'(5).
1 Answers
Best Answer
carlosmenciaconcertverizoncenter Staff answered 3 years ago
carlosmenciaconcertverizoncenter Staff answered 3 years ago
To find the derivative of the function we will use Chain Rule:
(d)/(dx)[f(g(x))=f'(g(x))=g'(x)]
s'(x)=g'(f(x))f'(x)
Plug in x=5 to find s'(5).
s'(5)=g'(f(5))f'(5)
=g'(6)f'(5)
As wee see on graph of g(x) there is a sharp corner at x=6, so g(x) is not differentiable at x=6. s'(5) does not exist because g is not differetiable at 6.
Result:
s'(5) doesn't exist