contestada

h(x)=
8
1
​
x
3
−x
2
h, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 8, end fraction, x, cubed, minus, x, squared
What is the average rate of change of hhh over the interval -2\leq x\leq 2−2≤x≤2minus, 2, is less than or equal to, x, is less than or equal to, 2?h(x)=
8
1
​
x
3
−x
2
h, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 8, end fraction, x, cubed, minus, x, squared
What is the average rate of change of hhh over the interval -2\leq x\leq 2−2≤x≤2minus, 2, is less than or equal to, x, is less than or equal to, 2?

Respuesta :

MrRoyal

The average rate of change of the function over −2 ≤ x ≤ 2 is 1/2

How to determine the average rate of change?

The function is given as:

[tex]h(x) = \frac 18x^3 - x^2[/tex]

The interval is given as:

−2 ≤ x ≤ 2

Calculate h(2) and h(-2)

[tex]h(2) = \frac 18 * 2^3 - (2)^2[/tex]

h(2) = -3

[tex]h(-2) = \frac 18 * (-2)^3 - (-2)^2[/tex]

h(-2) = -5

The average rate of change is then calculated as:

[tex]m = \frac{h(-2) - h(2)}{-2-2}[/tex]

This gives

[tex]m = \frac{-5 + 3}{-4}[/tex]

Evaluate

m = 1/2

Hence, the average rate of change of the function over −2 ≤ x ≤ 2 is 1/2

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Complete question

[tex]h(x) = \frac 18x^3 - x^2[/tex]

What is the average rate of change of h over the interval −2 ≤ x ≤ 2

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