How to find net change

Question

A function is given.

f(x) = x³ − 7x²;    x = 0, x = 10

(a) Determine the net change between the given values of the variable.

(b) Determine the average rate of change between the given values of the variable.

Answer 1

a) The net change in the function f(x) over a interval x=[a,b] is

f(b)-f(a)

Here

f(x)=x^3-7x^2 and a=0,b=10

So net change is

f(10)-f(0) = 1000-7(100)-0=300

b) The rate of change is given as

(f(b)-f(a))/(b-a)= 300/(10-0)=30