The  statements about the local maximums and minimums for the given function are true Over the interval [2, 4], the local minimum is –8.Over the interval [3, 5], the local minimum is –8.Over the interval [1, 4], the local maximum is 0.
We have given statement,
Over the interval [1, 3], the local minimum is 0
Over the interval [2, 4], the local minimum is –8.
Over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0.
from the given graph we have to find the correct statement.
Lets discuss each option one by one
What is the maximum and minimum point?
A high point is called a maximum . A low point is called a minimum .
Over the interval [1, 3], the local minimum is 0
If we look at the graph. The minimum point is (3.4,-8). Therefore the local minimum is -8 not 0.This is a false statement.
Over the interval [2, 4], the local minimum is –8.
The given minimum point is(3.4, -8). Thus the  local minimum is -8 which is true Therefore this statement is true
Over the interval [3, 5], the local minimum is –8.
By the  given minimum point, the local minimum  is -8 which is true statement.
Over the interval [1, 4], the local maximum is 0.
If we see at the graph.
The maximum point given is (2,0).
Thus given  statement is true because local maximum is 0.
Over the interval [3, 5], the local maximum is 0.
There is no maximum point therefore this is false statement.
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