(This is a multipart question. I got the first two parts.. I need help with the third part.)

Find the inflection points off(x)=x?4??+x?3???3x?2??+2. Give the values ofxin increasing order.

A pointpat which the graph of a function changes concavity is called an inflection point. At the inflection point,f?????=0or is undefined.

(a) I got this part. These answers are correct.

To start this problem, we need to find the first and second derivatives off(x)=x?4??+x?3???3x?2??+2.

f????(x)=4x?3??+3x?2???6x

f?????(x)=12x?2??+6x?6

(b) (I also got this part.)

We foundf?????(x)=12x?2??+6x?6=0.

Now solve this equation forx.Give the values ofxin increasing order.

Answer: -1, 1/2

(c) THIS IS THE PART I NEED HELP WITH. CHOOSE 0 FOR EACH PART.

To determine the points are inection points we need to see if the sign of r"{x}=12x2+5x-a=n changes on either side. We need to nd out the sign of f " {Jr} within each intervai. e)x-c- 1:5ince{x+ 1}-c{1and{2x- 1}-:{Jthenf"[x} \f