Question

HELP!

For the polynomial function f(x) = x3 - 7x2 + 10x , what is the average rate of change over the interval [2 , 4]

Answer 1

The average rate of change of the given function over the interval [2, 4] is -4.

Explanation:

To find the average rate of change of a function f(x) over the interval [a, b], we should use the formula:

`\boxed{\textsf{Average rate of change}=(f(b)-f(a))/(b-a)}`

Given function:

`f(x) = x^3 - 7x^2 + 10x`

To find the average rate of change of the given function over the interval [2, 4], we need to first find the values of f(2) and f(4).

`\begin{aligned}f(2) &= (2)^3 - 7(2)^2 + 10(2)\\&= 8 - 7(4) + 10(2)\\&= 8 - 28 + 20\\&= -20 + 20\\&= 0\end{aligned}`

`\begin{aligned}f(4) &= (4)^3 - 7(4)^2 + 10(4)\\&= 64 - 7(16) + 10(4)\\&= 64 - 112 + 40\\&= -48+ 40\\&= -8\end{aligned}`

Substitute the values into the formula for the average rate of change over the interval [2, 4]:

`\textsf{Average rate of change} = (f(4) - f(2))/(4 - 2) = (-8-0)/(4-2)=(-8)/(2)=-4`

Therefore, the average rate of change of the given function over the interval [2, 4] is -4.