PreCalculus
posted by Ann on .
For the function
f(x)=3x^3−42x
Compute the difference quotient
[f(x+h)−f(x)]/h,h≠0
I checked my work like 3 times and still got [(2x^3)+(3hx^2)+(3xh^2)+(h^3)(42h)]/h
Is it wrong?

looks like you forgot that pesky 3 out front.
f(x+h) = 3(x+h)^3  42(x+h)
= 3x^3 + 9x^2h + 9xh^2 + 3h^3  42x  42h
f(x) = 3x^3  42x
subtract to get
9x^2h + 9xh^2 + 3h^3  42h
now divide by h to get
9x^2 + 9xh + 3h^2  42