##### Question

# A continuous function f, defined for all x , has the following properties:

A continuous function f, defined for all x , has the following properties:

1. f is decreasing

2. f is concave up

3.f(17)=-4

4.f'(17)=-1/4

Sketch a possible graph for f, and use it to answer the following questions about f.

A. For each of the following intervals, what is the minimum and maximum number of zeros f could have in the interval? (Note that if there must be exactly N zeros in aninterval, the minimum and maximum are both N.)

minimum maximum

-infinity<x<0 ?????? ??????

0<x<1 ?????? ??????

1<x<17 ?????? ??????

17<x<infinity ?????? ??????

B.Are any of the following possible values for f'(1) ? (Enter your answer as a comma-separated list, or enter 'none' if none of them are possible.)-3 ,-2 , -1,-1/5 ,0,1/5 ,1 ,2 ,3 .

f'(1)=???????

C. What happens to f as x —> -infinity?