Given the function g(x)=x^2-9x+16, determine the average rate of change of the function over the interval 1≤x≤6.
Accepted Solution
A:
The rate of change on interval 1≤x≤6 is -2Step-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≤6So, a=1b=6Now,[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 -2Keywords: Functions, Rate of ChangeLearn more about functions at:brainly.com/question/2344476brainly.com/question/2364381#LearnwithBrainly