Is f(x)=(x^2+2x-2)/(2x-4)f(x)=x2+2x22x4 increasing or decreasing at x=0x=0?

1 Answer
Dec 14, 2015

The function is decreasing.

Explanation:

If f'(0)<0, then f(x) is decreasing when x=0.
If f'(0)>0, then f(x) is increasing when x=0.

Find f'(x) using the quotient rule.

f'(x)=((2x-4)d/dx[x^2+2x-2]-(x^2+2x-2)d/dx[2x-4])/((2x-4)^2

f'(x)=((2x-4)(2x+2)-2(x^2+2x-2))/(4(x-2)^2)

f'(x)=(4x^2+4x-8x-8-2x^2-4x+4)/(4(x-2)^2

f'(x)=(2x^2-8x-4)/(4(x-2)^2

f'(x)=(x^2-4x-2)/(2(x-2)^2

f'(0)=(-2)/8=-1/4

Since -1/4<0, f(x) is decreasing when x=0.