Question

f(x)=x
3
−9xf, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x
What is the average rate of change of fff over the interval [1,6][1,6]open bracket, 1, comma, 6, close bracket

Answer 1

Answer:

One of the main applications of definite integrals is to find the average value of a function y=f(x) over a specific interval [a,b]. In order to find this average value, one must integrate the function by using the Fundamental Theorem of Calculus and divide the answer by the length of the interval. ¯f=1b−ab∫af(x)dx.

Answer 2

Step-by-step explanation:

Answer:

105

Explanations:

Given the function,

F(x) = x³-9x

Rate of change of the function is given by

d{f(x)}/dx = 3x²-9

Given the interval [1,6]

Rate of change can be gotten by subtracting the lower interval from the upper interval

f'(x) = 3x²-9

f'(1) = 3(1)²-9

f'(1) = 3-9 = -6

f'(6) = 3(6)²-9

f'(6) = 108 - 9

f'(6) = 99

Average rate of change of function = f'(6) - f'(1)

= 99-(-6)

= 99+6

= 105