Question

Find the average rate of change for f(x) = x^2 − 3x − 10 from x = −5 to x = 10.

A) -1
B) -2
C) 1
D) 2

Answer 1

D) 2

The average rate of change of f(x)

A(x) =2

Explanation:

Step(i):-

Given that the function f(x) = x² - 3x -10

Given x =a = -5 and y = b = 10

The average rate of change of f(x)

`A(x) = (f(b)-f(a))/(b-a)`

Step(ii):-

f(x) = x² - 3x -10

f(-5) = (-5)² - 3(-5) -10 = 25+15-10=30

f(10) = (10)² -3(10)-10 = 100 -30 -10 =60

The average rate of change of f(x)

`A(x) = (f(b)-f(a))/(b-a)`

`A(x) = (60-30)/(10-(-5))= (30)/(15) = 2`

A(x) =2