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