Question

Given the function g(x)=x^2-9x+16, determine the average rate of change of the function over the interval 1≤x≤6.

Answer 1

The rate of change on interval 1≤x≤6 is -2

Step-by-step explanation:

The formula for rate of change of function on interval a≤x≤b is given by:

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

Given function

$g(x)=x^2-9x+16$

The given interval is:

1≤x≤6

So,

a=1

b=6

Now,

$g(1) = (1)^2-9(1)+16\\=1-9+16\\=8$

$g(6) = (6)^2-9(6)+16\\=36-54+16\\=-2$

Putting the values in the formula

$Rate\ of\ change=\frac{f(6)-f(1)}{6-1}\\\\=\frac{-2-8}{5}\\\\=\frac{-10}{5}\\\\=-2$

The rate of change on interval 1≤x≤6 is -2

Keywords: Functions, Rate of Change

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