Question

-3 The function graphed above has: Positive derivative on the interval(s) (-2.5,1) Negative derivative on the interval(s) (0o,-5) U (1,-00) Get help: Video Points possible: 1 Unlimited attempts. Score on last attempt: (0.5, 0), Score in gradebook: (0.5, 0), Out of: (0.5, 0.5) Message instructor about this question Submit

Answer 1

Answer follows in the image.

We know that a function has positive derivative in the interval where the function is increasing Similarly , a function has negative derivative in the interval where the function is decreasing IN the given graph, the function is increasing in the interval (-2,.5, 1) , so, it has a positive derivative interval(-2.5,1) So, it has a positive derivative in the interval (-2.5,1) [your answer is correct] Now, we can see that the function is decreasing in the interval (- infinity , 2 . 5) and (1, infinity)[Note that we are looking into the x- axis not the y- axis] Since function isa decreasing in(- infinity, -2. 5) and (1. Infinity) we have that the function has negative derivative in (- infinity, -2.5) union (1, infinity).So, Positive derivative on the interval (-2.5, 1) Negative derivative on the internals: (- infinity, -2. 5) union(1/ infinity).[or you may simply separate these intervals with a comma that is).