Is f(x)=(-2x^3-6x^2-3x+2)/(2x-1)f(x)=−2x3−6x2−3x+22x−1 increasing or decreasing at x=0x=0?

1 Answer
Mia
Jun 16, 2016

Decreasing

Explanation:

We think about evaluating f(1)f(1) and f(0)f(0)
If f(1)-f(0)<0f(1)−f(0)<0 then it is decreasing
iff(1)-f(0)>0f(1)−f(0)>0 then it is increasing

Let's calculate f(1)f(1) and f(0)f(0)

f(1)=(-2(1)^3-6(1)^2-3(1)+2)/(2(1)-1)f(1)=−2(1)3−6(1)2−3(1)+22(1)−1

f(1)=(-2-6-3+2)/(2-1)f(1)=−2−6−3+22−1
f(1)=-9f(1)=−9

f(0)=(-2(0)^3-6(0)^2-3(0)+2)/(2(0)-1)f(0)=−2(0)3−6(0)2−3(0)+22(0)−1
f(0)=-2f(0)=−2

We have: f(1)-f(0)=-9-(-2)=-9+2=-7f(1)−f(0)=−9−(−2)=−9+2=−7
So,f(1)-f(0)<0f(1)−f(0)<0

f(1)<f(0)f(1)<f(0)
So, the function is decreasing.

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