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

Answer:

-1

Step-by-step explanation:

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

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

so,

$\frac{f(5)-f(0)}{5-0}\\ f(5) = 5^3 - 6(5^2) + 4(5) + 7\\= 2\\f(0) = 7\\\frac{2-7}{5}=\frac{-5}{5}=-1$