Blog 2

Soooo we learned about derivatives and stuff in class this week. There are only two formulas you need to know so it aint that hard.

the two formulas are

f(x+dx)-f(x)/(dx) - secant line

lim as x -> 0 f(x+dx)-f(x)/(dx) - tangent line

the slope of a tangent line is the derivative of something.

Example:

Find the slope of the graph of f(x) = x^2 + 3x + 1 at (1, 3)

lim as Dx approaches 0: ( f(x + Dx) - f(x) ) / (Dx)

What you have to do is plug in (x+ Dx) for every x in the formula.

(x + Dx)^2 + 3(x + Dx) + 1 - (x^2 + 3x + 1) / (Dx)

That simplifies to...

x^2 + 2xDx + Dx^2 + 3x + 3Dx + 1 - x^2 - 3x -1 / Dx

2xDx + Dx^2 + 3Dx / Dx

2x + Dx + 3

plug in 0 for Dx

2x + 3 is your equation

Now just plug in the x coordinate to find the slope.

2(1) + 3 = 5

The slope is 5.

wellll i dont know how many words this is supposed to be so someone let me know. have a fun monday people.