Question

What is the average rate of change for the function f(x) = x^3 − 6x^2 + 4x +7 over the interval 0≤x≤5?

Answer 1

-1

Explanation:

The average rate of change of f(x) is slope because

`\frac{\int\limits^b_a {((d)/(dx)f(x)) } \, dx }{b-a}=(f(b)-f(a))/(b-a)`

so,

`(f(5)-f(0))/(5-0)\\ f(5) = 5^3 - 6(5^2) + 4(5) + 7\\= 2\\f(0) = 7\\(2-7)/(5)=(-5)/(5)=-1`