Based on the graph of f(x) in the figure, determine where f?(x)<0. A coordinate

Question

Based on the graph of f(x) in the figure, determine where f?(x)<0.

A coordinate plane has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. From left to right, a curve falls in quadrant 2 passing through a left-parenthesis negative 8 comma 6 right-parenthesis, falls to a minimum in quadrant 3 at left-parenthesis negative 6 comma negative 8 right-parenthesis, rises to a maximum at left-parenthesis negative 3 comma negative 4 right-parenthesis, falls to a minimum at left-parenthesis negative 1 comma negative 6 right-parenthesis, and rises passing through left-parenthesis 1 comma negative 6 right-parenthesis. All coordinates are approximate.

Select the correct answer below:

(??,?6)?(?6,?3)

(??,?6)?(?3,?1)

(?6,?3)?(?1,?)

(??,?)

Explanation / Answer

graph is decreasing till the point (-6,-8)
then it increases till the point (-3, -4)
then it decreases till the point (-1, -6)

f’(x) is less than 0 when graph is decreasing
so, it will be less than 0 for x=-inf to x=-6
again it will be less than 0 for x=-3 to x=-1
So, the answer is:
(-inf, -6) U (-3, -1)

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