Question

Find the value of constant k so that the average rate of change in f(t) on the indicated interval is the value provided, or indicate that no such value of k exists F(t) = kt^2; ARC = 1.5 on [-1, 2]

Answer 1

The averege rate of f(x) on the interval [a, b] is

`\text{Ave}\mathrm{}=(f(b)-f(a))/(b-a)`

Since the given interval is [-1, 2], then

a = -1, b = 2

Since the function is

`f(t)=kt^2`

Since the average is 1.5

Substitute them in the rule above

`\begin{gathered} 1.5=(k(2)^2-k(-1)^2)/(2--1) \\ 1.5=(4k-k)/(2+1) \\ 1.5=(3k)/(3) \\ 1.5=k \end{gathered}`

The value of k is 1.5