(Can someone work out this problem so I know how to do this type of problem?)
Find the average rate of change of f(x) =-x^3 + 1:
a) from 0 to 2
b) from 1 to 3
c) from -1 to 1

Question

(Can someone work out this problem so I know how to do this type of problem?)
Find the average rate of change of f(x) =-x^3 + 1:
a) from 0 to 2 
b) from 1 to 3
c) from -1 to 1

ash2326 · Answer

@HeyMolli I'll show you how to find the average rate of change for a
You do it for b and c then :)

ash2326 · Answer

Average Rate of f(x) from x=a to b is defined as
$$Rate=\frac{f(b)-f(a)}{b-a}$$
we have 
$$f(x)=-x^3+1$$
a) 0 to 2
Let's find f(2), put x=2 in f(x)
$$f(2)=-2^3+1=-8+1=-7$$

$$f(0)=-0+1=1$$
so
$$Rate=\frac{f(2)-f(0)}{2-0}\ \ \ \ \ \ \ \ \ \ \ =\frac{-7-1}{2-0} \ \ \ \ \ \ =-4$$
so average rate of change is -4
Do you understand this?

anonymous · Answer

Yes! Thank you!

ash2326 · Answer

Could you try to find the rate for the other two options?

anonymous · Answer

okay, i think b is -9.6, and c is -1.

ash2326 · Answer

check b again, c is correct

anonymous · Answer

Okay, well, if f(3) is -26 and f(1) is zero, then it's -26/(3-1), which is -26/2, so -13. Maybe?

ash2326 · Answer

yeah :) good

anonymous · Answer

awesome, thanks so much!