How do you find points of inflection on a graph of f'

  find the extrema of f'

Step-by-step explanation:

Points of inflection on a graph of f(x) are where the concavity changes from up to down, or vice versa. These are points where the second derivative is zero. On a graph of the first derivative, f'(x), those will be points where the slope of f'(x) is zero: extreme points (maxima or minima).

The slope of f'(x) may also be zero at a flat spot, but that will not be a point of inflection of f(x), because the sign of the slope does not change there.

__

By way of illustration, we show a graph of f' (red) and the corresponding function f(x) (dashed green). The marked points are where the slope of f' is zero. Only the right-most of those represents a point of inflection of f(x).

entering that problem on the tube might get you an answer

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.