Question

Analyze the graphed function to find the local minimum and the local maximum for the given function. Which statements about the local maximums and minimums for the given function are true? Check all that apply. Over the interval [–1, 1,] the local minimum is –8. 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. Over the interval [3, 5], the local maximum is 0.

Answer 1

Statement 1 is correct
Over the interval $x=-1$ and $x=1$ as shown in the diagram below, we can see that the minimum is at -8

Statement 2 is incorrect
Over the interval 1 and 3, we have a maximum of 0

Statement 3 is incorrect
Over the interval 2 and 4, we have a minimum of -8

Statement 4 is correct
Over the interval 3 and 5, we have a minimum of -8

Statement 5 is correct
Over interval 1 and 4, we have a maximum of 0

Statement 6 is incorrect
Over interval 3 and 5, we do not have a maximum

Answer 2

Lowest points those have bumps on them (0.6,-8) and (3.4,-8)

And highest point that has bump on it is (2,0)

Therefore,

Local minimum at x=0.6 is -8 and at x=3.4 is -8.

And local maxima is at x=2 is 0.

Therefore, following statements are applicable:

Over the interval [–1, 1,] the local minimum is –8.

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.