# Math Help - Slope of a polynomial function

1. ## Slope of a polynomial function

Hello Friends,
I need help on this problem
Directions: use equation one to find g '(x) [g '(x) is the slope]
equation one :
g' (x) = lim h->0 g(x+h) - g(x) all over h.
Then it says:
Recall the Difference quotient D.Q. = g(x+h) - g(x) all over h

The actual problem is g(x) = 3xsquared - 2x
sorry about the squared. I couldn't put a little two
Thanks,

2. Originally Posted by xArtist545
Hello Friends,
I need help on this problem
Directions: use equation one to find g '(x) [g '(x) is the slope]
equation one :
g' (x) = lim h->0 g(x+h) - g(x) all over h.
Then it says:
Recall the Difference quotient D.Q. = g(x+h) - g(x) all over h

The actual problem is g(x) = 3xsquared - 2x
sorry about the squared. I couldn't put a little two
Thanks,
Hi

$g(x) = 3x^2 - 2x$

$\frac{g(x+h) - g(x)}{h} = \frac{\left(3(x+h)^2 - 2(x+h)\right) - \left(3x^2 - 2x\right)}{h}$

Expand

$\frac{g(x+h) - g(x)}{h} = \frac{6 xh + 3h^2 - 2h}{h} = 6x + 3h - 2$

Therefore $g'(x) = \lim_{h \rightarrow 0} \frac{g(x+h) - g(x)}{h} = 6x - 2$

3. thanks