Question

let f(x)= 3x^3...what is f(a+h)−f(a)/h

Answer 1

\[\frac{3(a+h)^3-3a^3}{h}\]

Answer 2

so your main job is to cube
\[(a+h)^3=a^3+3a^2h+3ah^2+h^3\]

Answer 3

so you get
\[\frac{3(a^3+3a^2h+3ah^2+h^3)-3a^3}{h}\] you good from there?

Answer 4

3a^2 +9a^2h + 9ah^2-3a^ over h ??

Answer 5

yes, then note that
\[a^3-a^3=0\] and then cancel and h from each term

Answer 6

\[\frac{9a^2h+9ah^2+3h^3}{h}\]
\[9a^2+9ah+3h^2\]

Answer 7

thanks for the help