Question

AT WHAT X-VALUE DOES A
RELATIVE MINIMUM
OCCUR?

Answer 1

The graph was too small for me to see so I used the first derivative test to find it:

The answer is 4.24

(Super long explanation, my work is below):

For this test, first you find the derivative of the function, then you set that value to 0 and find the x values. This gives you the critical points, which you can use to test the intervals on the graph. Since this function has an open interval we can use - infinity and infinity as the endpoints of out test. When the value of derivative changes from a negative interval to a positive interval, that is a relative min.

Answer 2

x ≈ 4.239

Explanation:

A relative minimum is found at the bottom of any U-shape on the graph. If you expand the graph shown until it has a suitable scale, it can show you the relative minimum occurs at x ≈ 4.239.

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Additional comment

The relative maximum occurs at the top of any ∩-shape. The graphing calculator can show you that occurs at x ≈ -1.573.