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:
[tex]Rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]
Given function
[tex]g(x)=x^2-9x+16[/tex]
The given interval is:
1≤x≤6
So,
a=1
b=6
Now,
[tex]g(1) = (1)^2-9(1)+16\\=1-9+16\\=8[/tex]
[tex]g(6) = (6)^2-9(6)+16\\=36-54+16\\=-2[/tex]
Putting the values in the formula
[tex]Rate\ of\ change=\frac{f(6)-f(1)}{6-1}\\\\=\frac{-2-8}{5}\\\\=\frac{-10}{5}\\\\=-2[/tex]
The rate of change on interval 1≤x≤6 is -2
Keywords: Functions, Rate of Change
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