00:01
In this question, a function is given that is fx equals to x square lnx.
00:05
And we have to find out the inflection points of this function fx.
00:10
So no problem.
00:11
For this, we will want second derivative, but we will start from the first derivative and we will differentiate it with respect to x.
00:20
So f -dash -x, it will be differentiation of x square l -n -x.
00:23
And f -dash -x, it will be, it is a product of two functions.
00:28
So we will use the product rule here and we will take first one out and differentiation of second one plus second one out and differentiation of first one.
00:37
So f -dash -x it will be x square differentiation of lnx that is 1 by x plus lnx and dot differentiation of x squared that is 2x.
00:48
So over f -dash -x it will be x plus it will be 2x lnx.
00:56
Okay so this will be our first derivative okay and now we can say f -x will be we can x common factor and it will be one plus two then x okay and now we have to find out the second derivative then we will again differentiate it with respect to x so second derivative again there are two functions okay so we will first of all i'm writing down what we have to do okay we have to do the differentiation of this so so it is a product of two functions.
01:28
So we will use again the product rule...