Question

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.

Answer 1

@amistre64 @CausticSyndicalist @dan815 @dtan5457 @jagr2713 @mathmate @myininaya @perl @Preetha @quickstudent @sleepyjess @TheSmartOne @TheRaggedyDoctor

Answer 2

Starting from x=-2, is the function f(x) increasing or decreasing?

Answer 3

@familyguymath ?

Answer 4

first inc second dec then lastly inc again

Answer 5

What you just gave me is for f'(x).
If you need to find the absolute minimum, you need to find at which points f(x) (i.e. the function itself) is increasing.
I'll give you an example:

You will see that a minimum of the function (f(x)) occurs when the slope (f'(x)) changes from negative to positive. And conversely a maximum of the function (f(x)) occurs when the slope changes from positive to negative.