Simplify the difference Quotient?

(f(2+h) -f(2))/hf(2+h)−f(2)h if h is not 0

f(x) = x^2-6xf(x)=x2−6x

2 Answers
Somebody N.
Feb 18, 2018

h-4h−4

Explanation:

((2+h)^2-6(2+h)-(-8))/h(2+h)2−6(2+h)−(−8)h

(4+4h+h^2-12-6h+8)/h4+4h+h2−12−6h+8h

(h^2-2h)/hh2−2hh

h-h−2

iceman
Feb 18, 2018

h-2h−2

Explanation:

f(x)=x^2-6xf(x)=x2−6x

[f(x+h)-f(x)]/hf(x+h)−f(x)h
=[(x+h)^2-6(x+h)-(x^2-6x)]/h=(x+h)2−6(x+h)−(x2−6x)h
=(x^2+2xh+h^2-6x-6h-x^2+6x)/h=x2+2xh+h2−6x−6h−x2+6xh
=(2xh+h^2-6h)/h=2xh+h2−6hh
=[h(2x+h-6)]/h=h(2x+h−6)h
=2x+h-6=2x+h−6

[f(2+h)-f(2)]/hf(2+h)−f(2)h
=2*2+h-6=2⋅2+h−6
=h-2=h−2

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