Calculus and AnalysisThe graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(J(x)).
2 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).
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Best Answer
carlosmenciaconcertverizoncenter Staff answered 2 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
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