Find the quotient where h cannot equal 0

Question

For g(x) = 9 -x^2, find the quotient g(-6+h) - g(-6) all over h where h cannot equal zero.

(g(-6+h) - g(-6))/h = _____?

Answer 1

g'(x) = -2x

g'(-6) = -2(-6) = 12

g(x+h) - g(x) = 9-(x+h)^2 - 9 +x^2 = -2hx -h^2

all divided by h = -2x -h

g(-6+h)-g(-6)]/2 = -2(-6) -h = 12 +h

or

g(-6) = 9-(-6)^2 = 9-36 = - 27

g(-6+h) = 9- (-6+h)^2 = 9-(36 -12h +h^2) = 9-36 +12h - h^2 -9 + 36= 12h +h^2

g(-6+h)-g(-6) = 12h +h^2

[g(-6+h) -g(-6)]/h = 12 +h