Question

ww5: problem 14 (1 point) results for this submission entered answer preview result -2 -2 incorrect the answer above is not correct. use the figures below to evaluate the indicated derivative, or state that it does not exist. if the derivative does not exist, enter dne in the answer blank. the graph to the left (in black) gives f(x), while the graph to the right gives g(x) (which is constant for values of x greater than 60). f(x) g(x) \\(\frac{d}{dx}fg(x)|_{x = 30}=\\) (if the derivative does not exist, enter dne.) preview my answers submit answers your score was recorded. you have attempted this problem 1 time. you received a score of 0% for this attempt. your overall recorded score is 0%. you have unlimited attempts remaining.

Explanation:

Step1: Recall chain - rule

The chain - rule states that if $y = f(g(x))$, then $y^\prime=f^\prime(g(x))\cdot g^\prime(x)$.

Step2: Evaluate $g(30)$

From the graph of $g(x)$, find the value of $g(30)$. Assume from the graph that $g(30)$ is some value $a$.

Step3: Find $g^\prime(30)$

The derivative of a constant function is $0$. Since $g(x)$ is constant for $x > 60$ and we assume a smooth behavior around $x = 30$, if $g(x)$ is linear or constant - like in the relevant region, $g^\prime(30)=0$.

Step4: Calculate the derivative of the composite function

By the chain - rule $\frac{d}{dx}f(g(x))\big|_{x = 30}=f^\prime(g(30))\cdot g^\prime(30)$. Since $g^\prime(30) = 0$, then $\frac{d}{dx}f(g(x))\big|_{x = 30}=0$.

Answer:

$0$