Question

Use the graph to find the following.

Answer 1

The values of x at wich F(x) has local minimums are x = -2 and x = 4, and the local minimums are:

• F(-2) = -3
• F(4) = -5

What is a local maximum/minimum?

A local maximum is a point on the graph of the function, such that in a close vicinity it is the maximum value there. So, on an interval (a, b) a local maximum would be F(c) such that:

c ∈ (a, b)

F(c) ≥ F(x) for ∀ x ∈ [a, b]

A local minimum is kinda the same, but it must meet the condition:

c ∈ (a, b)

F(c) ≤ F(x) for ∀ x ∈ [a, b]

A) We can see two local minimums, we need to identify at which values of x do they happen.

The first local minimum happens at x = -2

The second local minimum happens at x = 4.

B) The local minimums are given by F(-2) and F(4), in this case, the local minimums are:

• F(-2) = -3
• F(4) = -5

If you want to learn more about minimums/maximums, you can read:

brainly.com/question/2118500