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Elena-2011 [213]
2 years ago
13

Given the function f(x) = x² + 3x - 2 What is the average rate of change for the function from 2 to 6? Show your work.

Mathematics
1 answer:
11Alexandr11 [23.1K]2 years ago
7 0

The average rate of change is 11

Explanation:

The given function is f(x)=x^{2}+3 x-2

We need to determine the average rate of change for the function from 2 to 6

The average rate of change can be determined using the formula,

\frac{f(b)-f(a)}{b-a}

where a=2 and b=6

Now, we shall determine the values of f(2) and f(6) by substituting the values for x = 2 and x = 6 in the function f(x)=x^{2}+3 x-2

Thus, we have,

f(2)=2^{2}+3 (2)-2

       =4+6-2

f(2)=8

Similarly, substituting x = 6, we get,

f(6)=6^{2}+3 (6)-2

       =36+18-2

f(6)=52

Hence, substituting these values in the formula \frac{f(b)-f(a)}{b-a} , we get,

\frac{f(b)-f(a)}{b-a}=\frac{52-8}{6-2}

Simplifying, we get,

\frac{f(b)-f(a)}{b-a}=\frac{44}{4}=11

Thus, the average rate of change for the function from 2 to 6 is 11

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