Question

HELP WITH CALCULUS ASAP!!

The figure below shows the graph of f ', the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4.

Find the x-value where f attains its absolute minimum value on the closed interval from x = -2 to x = 6. Justify your answer. (10 points)

Appreciate it, Thank you so much :)

Answer 1

Answer: x = 5

Explanation: To find the where the absolute minimum of f occurs from f', we can find where f' changes from negative to positive.

Think about it this way: an absolute minimum on f would look like a "U", meaning that the function would decrease and then increase. In other words, the slope would change from negative to positive.

So, if we find where f' changes from negative to positive, we can find where the absolute minimum occurs. The only x-value where this occurs on f' is x = 5.