Question

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?

Answer 1

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