Question

Find the indicated quantities for f(x)=3x^2

The average rate of change of f(x) if x changes from 1 to 4

Answer 1

\[\frac{f(4)-f(1)}{4-1}\] is what you need to compute

Answer 2

\[f(4)=3\times 4^2=48, f(1)=3\times 1^2=3\] you get
\[\frac{48-3}{3}=\frac{45}{3}=15\]

Answer 3

\[\Delta f=f(x_1)-f(x_0)\]\[\Delta x=x_1-x_0\]
The average rate of change is \(\frac{\Delta f(x)}{\Delta x}\)