derivative

f′(x)=limh−>0f(x+h)−f(x)h f'(x) = lim_{h->0} \frac{f(x+h)-f(x)}{h}

g′(x)=limx−>tg(x)−f(t)x−t g'(x) = lim_{x->t} \frac{g(x)-f(t)}{x-t} same as . g′(x)=limx−>tg(t−h)−g(t)h g'(x)=lim_{x->t}\frac{g(t-h)-g(t)}{h}

Slope Forms

  1. Point Slope Form: y−y1=m(x−x1) y-y_1 = m(x-x_1)

  2. Slope Intercept Form: y=mx+b y = mx + b

  3. Standard Form: Ax+By=C Ax + By = C

m describes the slope, b describes the y-intercept

Example: (-3, 6)(6, 0)

m=>0−66−(−3)=−69=−23 m => \frac{0-6}{6-(-3)} = -\frac{6}{9} = -\frac{2}{3}

  1. y−6=−23(x+3) y-6 = -\frac{2}{3}(x+3)

  2. y−6=−23x−2=>y=−23x+4 y-6 = -\frac{2}{3}x-2 => y = -\frac{2}{3}x + 4

  3. 23x+y=4 \frac{2}{3}x + y = 4

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