Question

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Answer 1

The interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].

Option D) is the correct answer.

Over which interval does f have a positive rate of change?

To determine whether the average rate of change is positive, f(max) - f(min) must be greater than zero.

Given the function; f(x) = x³ - 9x

We determine f(max) - f(min)

At interval [ -2, 1 ]

(x³ - 9x) - ( x³ - 9x )

( (1)³ - 9(1) ) - ((-2)³ - 9(-2))= -8 - 10 = -18 NOT POSITIVE

At interval [ -2, 3 ]

(x³ - 9x) - ( x³ - 9x )

( (3)³ - 9(3) ) - ((-3)³ - 9(-3))= 0 - 0 = 0 NOT POSITIVE

At interval [ -1, 2 ]

(x³ - 9x) - ( x³ - 9x )

( (2)³ - 9(2) ) - ((-1)³ - 9(-1))= -10 - 8 = -18 NOT POSITIVE

At interval [ -4, -1 ]

(x³ - 9x) - ( x³ - 9x )

( (-1)³ - 9(-1) ) - ((-4)³ - 9(-4))= 8 - (-28) = 36 POSITIVE

Therefore, the interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].

Option D) is the correct answer.

Learn more about average rate of change: brainly.com/question/23715190

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