Calculus question

Question

I'm having problems finding an answer to the following question:

 

Find the average rate of change for the following function: f(x)=4x^3-3x^2+1 between x=-3 and x=2.

 

I'd appreciate not only an answer, but how you solved it.

 

Thanks!

Answer 1

Hi,

Average rate of change between x=-3 and x=2

is just the normal slope you known before

[f(-3)-f(2)]/[-3-2] ===> this is slope

now we just plug in

[4(-3)³-3(-3)²+1-4(2)³+3(2)²-1]/(-5)   ==> 1 cancels

[4(-27)-3(9)-4(8)+3(4)]/(-5)

[-108-27-32+12]/(-5)

-155/(-5)

31