The graph of a function fis given 0 2s 3s 4s Consider the function below when an

Question

The graph of a function fis given 0 2s 3s 4s Consider the function below when answering the following questions. g(x)-(t) dr (a) 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.) 1min= 16 x2min= 32 X1max x2max= 24 (b) Where does g attain its absolute maximum value? x= 16 (c) On what intervals is g concave downward? (Enter the intervals that contain smaller numbers first.)

Explanation / Answer

g'(x) =f(x)

for local extremum g'(x)=f(x)=0

f(x) changes from negative to positive at  3s/2,7s/2 , positive to negative at  s/2,5s/2

g(x) has local minimum at x= 3s/2,7s/2 and local maximum at x= s/2,5s/2

g(x) has local minimum at x= 6,14 and local maximum at x= 2,10

(a)

x1min=6,x2min=14,x1max=2,x2min=10,

(b)

absolute maximum value at x=(9/2)s

absolute maximum value at x=18

(c)

g(x) is concave downward when f(x) is decreasing

f(x) is decreasing in (s/4,s)U(2s,3s)U(4s,9s/2)

g(x) is concave downward in (1,4)U(8,12)U(16,18)

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