f′(x)=limh−>0f(x+h)−f(x)h f'(x) = lim_{h->0} \frac{f(x+h)-f(x)}{h} f′(x)=limh−>0hf(x+h)−f(x)
g′(x)=limx−>tg(x)−f(t)x−t g'(x) = lim_{x->t} \frac{g(x)-f(t)}{x-t} g′(x)=limx−>tx−tg(x)−f(t) same as . g′(x)=limx−>tg(t−h)−g(t)h g'(x)=lim_{x->t}\frac{g(t-h)-g(t)}{h} g′(x)=limx−>thg(t−h)−g(t)
Point Slope Form: y−y1=m(x−x1) y-y_1 = m(x-x_1) y−y1=m(x−x1)
Slope Intercept Form: y=mx+b y = mx + b y=mx+b
Standard Form: Ax+By=C 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} m=>6−(−3)0−6=−96=−32
y−6=−23(x+3) y-6 = -\frac{2}{3}(x+3) y−6=−32(x+3)
y−6=−23x−2=>y=−23x+4 y-6 = -\frac{2}{3}x-2 => y = -\frac{2}{3}x + 4 y−6=−32x−2=>y=−32x+4
23x+y=4 \frac{2}{3}x + y = 4 32x+y=4
Last updated 6 years ago
