Derivatives

The slope generator/definition of a deriative

lim x→0 f(x+h) - f(x) / h

Point slope form

y-y₁ = (x-x₁)

General Form

Ax + By = C

slope intercept form

y = mx + b

solve for (x+h)²

x²+2xh+h²

Steps for using the slope generator

1. Plug

2. Get rid of parenthesies

3. Combine like terms

4. factor and then cancel

Solve for point slope given f(x) = 2x² +4x - 3 with lim h → 0

STEPS

1) 2(x+h)²+4(x+4)-3-(2x²+4x-3)/h

2)2x²+4xh+2h²+4x+4h-3-2x²-4x+3/h

3)4xh +2h²+4h/h

4) lim h→0 3x+4

DON’T FORGET lim h→0