# Math Help - tangent lines

1. ## 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?

2. ## Re: tangent lines

Originally Posted by dwsmith
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?
$h(x) = f[g(x)]$

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

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

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