Question

Create one function that satisfies all the following conditions and explain your choices:

-The instantaneous rate of change at x=2 is zero

-The instantaneous rate of change at x=3 is negative

-The average rate of change on the interval [0,4] is zero

Answer 1

I really dont know but if i did i would tell you and i will try and find out

Answer 2

f' = a(x-2)
f'(3) < 0, so a < 0
f' = 2-x
f = 2x - x^2/2 + c
or, how about
f(x) = 4x-x^2+c
(f(4)-f(0))/(4-0) = 0
so f(4) = f(0)
16-16+c = 0-0+c
works for any c, so let's use c=0

f(x) = 4x-x^2