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Consider the function given by f(x)= x² +3. Find its average rate of change from x = -2 to x = 4.
Carefully show the work that leads to your final answer.

Sagot :

MrRoyal

Answer:

[tex]Rate = 2[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2 + 3[/tex]

Required

Determine the average rate of change from -2 to 4

This is calculated using:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

In this case:

[tex]a = -2[/tex]

[tex]b = 4[/tex]

So, we have:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

[tex]Rate = \frac{f(4) - f(-2)}{4 - (-2)}[/tex]

[tex]Rate = \frac{f(4) - f(-2)}{4 +2}[/tex]

[tex]Rate = \frac{f(4) - f(-2)}{6}[/tex]

Calculate f(4):

[tex]f(x) = x^2 + 3[/tex]

[tex]f(4) = 4^2 + 3[/tex]

[tex]f(4) = 19[/tex]

Calculate f(-2)

[tex]f(x) = x^2 + 3[/tex]

[tex]f(-2) = (-2)^2 + 3[/tex]

[tex]f(-2) = 7[/tex]

So:

[tex]Rate = \frac{f(4) - f(-2)}{6}[/tex]

[tex]Rate = \frac{19-7}{6}[/tex]

[tex]Rate = \frac{12}{6}[/tex]

[tex]Rate = 2[/tex]

The average rate of change is 2.

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