What are the points of inflection of #f(x)=xcos^2x + x^2sinx #?

1 Answer
Topscooter
Dec 18, 2015

The point #(0,0)#.

Explanation:

In order to find the inflection points of #f#, you have to study the variations of #f'#, and to do that you need to derivate #f# two times.

#f'(x) = cos^2(x) + x(-sin(2x) + 2sin(x) + xcos(x))#

#f''(x) = -2sin(2x) + 2sin(x) + x(-2cos(2x) + 4cos(x) - xsin(x))#

The inflection points of #f# are the points when #f''# is zero and goes from positive to negative.

#x = 0# seems to be such a point because #f''(pi/2) > 0# and #f''(-pi/2) < 0#

Related questions
See all questions in Determining Points of Inflection for a Function
Impact of this question
1518 views around the world
You can reuse this answer
Creative Commons License