Question

Determine the average rate of change of f(x)=2x2−11 over the interval [−3, 3] .

Answer 1

The average rate of change of the function f(x) = $2x^2-11$ over the interval [-3, 3] is 0

The function is

f(x) = $2x^2-11$

The average rate of change = $\frac{f(b)-f(a)}{b-a}$

First we have to find each values and substitute the values in the equation.

The interval = [-3, 3]

The value of a = -3

The value of b = 3

To find the value of f(-3), substitute the value of x = -3 in the given function

f(-3) = $2(-3)^2-11$

= 2×9 - 11

= 18-11

= 7

The value of f(b) = $2(3)^2-11$

= 2×9 - 11

= 18-11

= 7

The average rate of change = $\frac{7-7}{3--3}$

= 0/6

= 0

Hence, the average rate of change of the function f(x) = $2x^2-11$ over the interval [-3, 3] is 0

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