Question

Consider the function given by f(x)= x² +3. Find its average rate of change from x = -2 to x = 4.

Answer 1

Answer:

$Rate = 2$

Step-by-step explanation:

Given

$f(x) = x^2 + 3$

Required

Determine the average rate of change from -2 to 4

This is calculated using:

$Rate = \frac{f(b) - f(a)}{b - a}$

In this case:

$a = -2$

$b = 4$

So, we have:

$Rate = \frac{f(b) - f(a)}{b - a}$

$Rate = \frac{f(4) - f(-2)}{4 - (-2)}$

$Rate = \frac{f(4) - f(-2)}{4 +2}$

$Rate = \frac{f(4) - f(-2)}{6}$

Calculate f(4):

$f(x) = x^2 + 3$

$f(4) = 4^2 + 3$

$f(4) = 19$

Calculate f(-2)

$f(x) = x^2 + 3$

$f(-2) = (-2)^2 + 3$

$f(-2) = 7$

So:

$Rate = \frac{f(4) - f(-2)}{6}$

$Rate = \frac{19-7}{6}$

$Rate = \frac{12}{6}$

$Rate = 2$

The average rate of change is 2.