Question

3. [2 points] Let $f$, $g$, $h$ be differentiable functions defined for all values of $x$ with values given by $h(0) = 3$, $h'(0) = 0$, $h'(1) = 4$, $h(1) = 0$, $g(0) = 1$, $g'(0) = 2$, $f'(1) = 1$. If $y = f(g(h(x)))$, find $y'(1)$.

          3. [2 points]
Let $f$, $g$, $h$ be differentiable functions defined for all values of $x$ with values given by
$h(0) = 3$, $h'(0) = 0$, $h'(1) = 4$, $h(1) = 0$, $g(0) = 1$, $g'(0) = 2$, $f'(1) = 1$. If $y = f(g(h(x)))$, find $y'(1)$.

3. [2 points]
Let f, g, h be differentiable functions defined for all values of x with values given by
h(0) = 3, h'(0) = 0, h'(1) = 4, h(1) = 0, g(0) = 1, g'(0) = 2, f'(1) = 1. If y = f(g(h(x))), find y'(1).

Added by Linda C.

Applied Calculus for the Managerial, Life, and Social Sciences

Soo T. Tan 10th Edition

Chapter 3

Instant Answer

Solved by Expert Carson Merrill

Step 1

We are given that h'(0) = 0 and h'(1) = 4. This means that the derivative of h(x) is a linear function that passes through the points (0,0) and (1,4). We can write this derivative as h'(x) = 4x. Show more…

Show all steps

Thanks for your feedback!

Let f, g, h be differentiable functions defined for all values of x with values given by h(0)=3, h'(0)=0, h'(1)=4, h(1)=0, g(0)=1, g'(0)=2, f'(1)=1. If y=fg(h(x)), find y'(1).