f and g are differentiable functions s.t $\displaystyle h(x)=f(g(x))$. The equation of the tangent line at (2,5) at g is $\displaystyle y=3x-1$ at (5,1) at f is $\displaystyle y=4x-19$ What is h(2) and h'(2)? How do I find this?
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Originally Posted by dwsmith f and g are differentiable functions s.t $\displaystyle h(x)=f(g(x))$. The equation of the tangent line at (2,5) at g is $\displaystyle y=3x-1$ this says g(2) = 5 and g'(2) = 3 at (5,1) at f is $\displaystyle y=4x-19$ this says f(5) = 1 and f'(5) = 4 What is h(2) and h'(2)? How do I find this? $\displaystyle h(x) = f[g(x)]$ $\displaystyle h(2) = f[g(2)] = ?$ $\displaystyle h'(x) = f'[g(x)] \cdot g'(x)$ $\displaystyle h'(2) = f'[g(2)] \cdot g'(2) = ?$