Question

Find the average rate of change of f(x) = 4x^2 – 3 on theinterval [1, a]

Answer 1

Average rate of change is given by the equation

`(f(x2)-f(x1))/(x2-x1)`

x1=1

x2=a

Find f(1) and f(a)

`\begin{gathered} f(1)=4\cdot(1^2)-3=4-3=1 \\ f(a)=4\cdot a^2-3=4a^2-3 \end{gathered}`

Find the average rate of change

`((4a^2-3)-1)/(a-1)=(4a^2-4)/(a-1)`

Factor

`(4a^2-4)/(a-1)=(4\cdot(a-1)\cdot(a+1))/(a-1)=4\cdot(a+1)=4a+4`

The average rate of change is 4a + 4 on the interval [1,a]