Question

Let ​ f(x)=x2+5x−8​.

What is the average rate of change from x = 2 to x = 6?

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Answer 1

just find the slope
that is ((f(6)-f(2))/(6-2)

f(6)=6^2+5(6)-8=36+30-8=58
f(2)=2^2+5(2)-8=4+10-8=6


average is (f(6)-f(2))/(6-2)=(58-6)/(4)=52/4=13

average rate of change is 13

Answer 2

Answer: 13

Explanation:

The average rate of change of a function f(x) from
`x_1` and
`x_2` is given by :-

`A=(f(x_2)-f(x_1))/(x_2-x_1)`

Therefore, for the given function
`f(x)=x^2+5x-8`, the average rate of change from x = 2 to x = 6 is given by :-

`A=(f(6)-f(2))/(6-2)\\\\=((6^2+5(6)-8)-(2^2+5(2)-8))/(4)\\\\=(58-6)/(4)\\\\=(52)/(4)=13\\\\\Rightarrow A=13`

Hence, the average rate of change from x = 2 to x = 6 is 13.