Question

f(x+h)-f(x) / h for f(x) = 3x^2 - x - 6

Answer 1

\[\frac{ f(x+h)-f(x) }{ h }\]

\[f(x) = 3x ^{2}-x-6\]

Answer 2

If it is just that function, then you can plug in (x+h) in the function F(x) and then simply subtract the equation f(x). This looks like a derivative problem, so if there is a
\[\lim_{h \rightarrow 0}\]
before that whole function, then the answer would be the derivative of the function f(x), which in this case is:
\[6x-1\]
If there is no limit, then you wind up with:
\[\frac{[(x+h)^2-(x+h)-6]- (3x^2-x-6)}{ h }\]
Which you can simplify by multiplying out the terms and adding like terms.

Answer 3

Do you mean:
\[\frac{ (3)(x+h)^{2}-(x+h)-6) - (3x ^{2}-x-6) }{ h }\]

Answer 4

Or the 3 cannot be included?

Answer 5

Yes you're right, I missed the three. Include it.

Answer 6

Can you help me solve. Lol. Im here having problem because Im getting a square.

Answer 7

So far, this is where I'm at:

Answer 8

\[\frac{ 3(x+h)^{2}-(x+h)-6-(3x ^{2}-x-6 }{ h }\]

So these will cancel out:

\[3x^{2}, -3x ^{2}, -x, -x, -6, -6\]

Leaving:

\[\frac{ 3h ^{2}+h }{ h }\]

How did I get \[3h ^{2}? --- 3(x+h)^{2} = 3x+3h ^{2}\]

Answer 9

3(x+h)^2 - (x+h) - 6 = 3(x^2+2xh+h^2) - x - h - 6
= 3x^2 + 6xh + 3h^2 - x -h - 6
subtract 3x^2 - x - 6:
3x^2 + 6xh + 3h^2 - x -h - 6
-3x^2 + x + 6
--------------------------------
6xh + 3h^2 -h

= h(3h + 6x - 1)

Answer 10

Divide by h, and it will cancel out the h in the numerator leaving you with:
(3h + 6x - 1)