F(x)= x^3 - 9xf(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?

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

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b. 153 students do not participate in sports and seventy-five 12th graders were surveyed