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ale4655 [162]
3 years ago
9

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

Mathematics
1 answer:
xxTIMURxx [149]3 years ago
6 0

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

<em>The average rate of change is 2.</em>

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