Question

Given f(x) = 2x2 - 4, find the average rate of change from x1 = -2 to x2 = 4.

Answer 1

The average rate of change = 4

Explanation:

Given the function

`f\left(x\right)\:=\:2x^2\:-\:4`

x₁=-2, x₂=4

f(x₁) = f(-2) = 2x²-4 = 2(-2)²-4 = 8-4 = 4

f(x₂) = f(4) = 2x²-4 = 2(4)²-4 = 32-4 = 28

The average rate of change = f(x₂) - f(x₁) / x₂ - x₁

= (28-4)/(4-(-2))

= 24/6

= 4

Thus, the average rate of change = 4