if f(x)= -2x^2-3x+2, find f(x+h)-f(x)\h where h does not equal 0

f(x+h)=-2(x+h)^2-3(x+h)+2

=-2(x^2+h^2+2xh)-3x-3h+2

=-2x^2-2h^2-4xh-3x-3h+2

f(x+h)-f(x)=-2x^2-2h^2-4xh-3x-3h+2+2x^2+3x-2

=-2h^2-4xh-3h

f(x+h)-f(x)/h=-2h-4x-3

h!=0 means h should be positive or negative but not zero.

(1) h is positive

-2h-4x-3>0

2h+4x+3<0

2h<-(4x+3)

h<-(4x+3)/2

h>(4x+3)/2

(2) h is negative

-2h-4x-3<0

2h+4x+3>0

h>-(4x+3)/2

h<(4x+3)/2

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