Question

Use the figure below to estimate the indicated derivatives, or state that they do not exist. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x = 2. The graph of g(x) is blue.

Answer 1

Answer:

Derivative $f'(x)$ does not exist at $x=2$ in (0,4)

and Derivative $g'(x)$ exists over (0,4)

Step-by-step explanation:

Given information

$h(x)=f(x).g(x)$

So, derivative

$h'(x)=f(x).g'(x)+g(x).f'(x)$

From the above equation

$f'(x)=3/2$ at  $0\leq x\leq 2$

$f'(x)=0$  at $x=2$

$f'(x)=-3/2$ at $2\leq x\leq 4$

From the graph

$f(x)$ is graph of absolute function at $x=2$

Hence, derivative does not exist at $x=2$ in (0,4)

Now $g(x)$ is the graph of straight line and derivative of straight line is constant  so, $g(x)$ is differential over (0,4).

$g'(x)$ exists over (0,4)

$g'(x)=-3/4$

Derivative does not exist at $x=2$ in (0,4)

For more information visit:

https://brainly.com/question/19726794?referrer=searchResults