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.

Derivative does not exist at in (0,4)

and Derivative exists over (0,4)

Step-by-step explanation:

Given information

So, derivative

From the above equation

at  

 at

at

From the graph

is graph of absolute function at

Hence, derivative does not exist at in (0,4)

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

exists over (0,4)

Derivative does not exist at in (0,4)

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f'(x) doesn't exist at x=2 in (0,4)

g'(x) exist over (0,4).

Step-by-step explanation:

We are given a graph and need to find the point derivative does not exist.

Black: Graph of f(x)

Blue: Graph of g(x)

In interval (0,4)

f(x) is graph of absolute function. At x=2, f(x) has vertex or corner.

As we know function is not differential at corner.

Hence, f'(x) doesn't exist at x=2 in (0,4)

g(x) is graph of straight line. Derivative of straight line is constant. g(x) is differential over (0,4)

Hence, g'(x) exist over (0,4).

i think the correct option is the second option.