# f(x)

• Jan 28th 2007, 01:54 PM
Mr_Green
f(x)
Let f(x) = x^2 - 3x - 4.

a.) Find the slope, m(h), of the secant line between the points A(1, f(1)) and B(1 + h, f(1 + h)).

*Here's what I've come up with so far.

f(1) = 1^2 - 3(1) - 4
f(1) = -6
So, A is the point (1, -6)

f(1 + h) = (1 + h)^2 - 3(1 + h) - 4
f(1 + h) = 1 + 2h + h^2 - 3 - 3h - 4
f(1 + h) = h^2 - h - 6
So, B is the point (1 + h, h^2 - h - 6)
• Jan 28th 2007, 09:51 PM
earboth
Quote:

Originally Posted by Mr_Green
Let f(x) = x^2 - 3x - 4.

a.) Find the slope, m(h), of the secant line between the points A(1, f(1)) and B(1 + h, f(1 + h)).

*Here's what I've come up with so far.

f(1) = 1^2 - 3(1) - 4
f(1) = -6
So, A is the point (1, -6)

f(1 + h) = (1 + h)^2 - 3(1 + h) - 4
f(1 + h) = 1 + 2h + h^2 - 3 - 3h - 4
f(1 + h) = h^2 - h - 6
So, B is the point (1 + h, h^2 - h - 6)

Hello,

Now use the formula to calculate the slope between 2 points $\displaystyle P_1(x_1, y_1) \text{ and } P_2(x_2, y_2)$
$\displaystyle m=\frac{y_2 - y_1}{x_2 - x_1}$ Plug in the coordinates you know:
$\displaystyle m=\frac{(h^2 - h - 6) - (-6)}{(1 + h) - 1}=\frac{h^2 - h }{ h}=\frac{h(h - 1) }{ h}=h-1$