Question

use the graph to determine the locations and type of the local extrema. write DNE for all extrema that do not exist. separate multiple answers with a comma, if necessary.local minimum at:local maximum at:

Answer 1

Local minimum at: (1, -7) , (3, -7).

Local maximum at : DNE

STEP - BY - STEP EXPLANATION

What to find?

Local extrema.

To solve the given problem, we will use the steps below:

Step 1

Give a definition of lacal extrema.

A local extremum of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.

OR

Local extrema on a function are points on the graph where the -coordinate is larger (or smaller) than all other -coordinates on the graph at points ''close to'' . A function has a local maximum at , if for every near .

Step 2

Locate the local extremum from the graph.

From the graph given, we have two local minimum.

At x = 1, f(1) =-7

Hence, the local minimum is (1, -7)

At x=3, f(3) =-7

Hence, the local minimum is ( 3, - 7)

Therefore, the local minimum are (1, -7) , (3, -7).

Observe from the graph that the local maximum do not exist.

Hence, local maximum = DNE