I\'m not sure why I\'m getting this wrong. I think it might be that I need to lo

Question

I'm not sure why I'm getting this wrong. I think it might be that I need to look at the derivative of the graph or something like that, but I'm not sure.

The graph of a function f is given Consider the function below when answering the following questions. At what values of x do the local maximum and minimum values of g occur? (Enter solutions from smallest to largest. If there are any unused answer boxes, enter NONE in the last boxes.) Where does g attain its absolute maximum value? On what intervals is g concave downward? (Enter the intervals that contain smaller number first.)

Explanation / Answer

a)

Since we are asked to find the max and min values of g, we need to look at the areas formed under the given f curve
Clearly, areas between say t = 4 to t = 12 , t = 20 to t = 28 are negative areas.

So, 12 and 28 will be the local minimum values

And areas over t = 0 to 4 , t = 12 to 20 and t = 28 to 36 are positive areas.

So, 4 and 20 are the local maximum values

x1min = 12
x2 min = 28
x1max = 4
x2max = 20

b)

Abs max value :

x = 36

c)

g would be concave down wherever f is decreasing in the positive direction

(2 , 8) U (16 , 24) U (32 , 36) ---> ANSWER

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