Question

find and simplify the difference quotient: f(x+h)-f(x) / h (h is not zero for the given function)

Answer 1

What have you tried so far?

Answer 2

dont even know where to start

Answer 3

f(x+h)+3x^2?

Answer 4

/ h

Answer 5

What is \(f(x)\) defined as?

Answer 6

oh sorry i left that out haha f(x) = -3x^2

Answer 7

Alright. You have it right so far:
\[\frac{f(x+h)-f(x)}{h}=\frac{f(x+h)+3x^2}{h}.\]
Now, put \(x+h\) where \(x\) is in \(-3x^2.\)

Answer 8

3(x+h)^2?

Answer 9

\(-3(x+h)^2\), but yes. Now simplify the top of that fraction and see if anything else can be done.

Answer 10

youre gonna have to write it out I cant picture it

Answer 11

\[\frac{-3(x+h)^2+3x}{h}\]
What can you do from here? Simplify \(-3(x+h)^2\). Then combine like terms. What do you get then?

Answer 12

h^2+x^2+2xh?

Answer 13

multiply that by -3?

Answer 14

Yup. Then what?