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Math Help - tangent lines

  1. #1
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    tangent lines

    f and g are differentiable functions s.t h(x)=f(g(x)).

    The equation of the tangent line at (2,5) at g is y=3x-1

    at (5,1) at f is y=4x-19

    What is h(2) and h'(2)?

    How do I find this?
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  2. #2
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    Re: tangent lines

    Quote Originally Posted by dwsmith View Post
    f and g are differentiable functions s.t h(x)=f(g(x)).

    The equation of the tangent line at (2,5) at g is y=3x-1

    this says g(2) = 5 and g'(2) = 3

    at (5,1) at f is y=4x-19

    this says f(5) = 1 and f'(5) = 4

    What is h(2) and h'(2)?

    How do I find this?
    h(x) = f[g(x)]

    h(2) = f[g(2)] = ?

    h'(x) = f'[g(x)] \cdot g'(x)

    h'(2) = f'[g(2)] \cdot g'(2) = ?
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