Question

Find the average rate of change for the function f(x) = 4x2 + 6 over the interval [1, 4].

Answer 1

20

Explanation:

To find the average rate of change of a function over an interval [a, b], you can use the following formula:

`Average\ Rate\ of\ Change=(f(b)-f(a))/(b-a)\\`

For the function f(x)=4x²+6 over the interval [1, 4], the average rate of change is:

Average Rate of Change=f(4)−f(1)4−1Average Rate of Change=4−1f(4)−f(1)​

`Average\ Rate\ of\ Change=(f(4)-f(1))/(4-1)\\=(4*4^2+6-(4*1^2+6))/(3) \\=(64-4)/(3) =20\\\\`

So, the average rate of change for the function f(x)=4x²+6 over the interval [1, 4] is 20.