Question

f(x)= x*(ln(x))^2. Find a constant c in (0,1) such that f'(c)=0

Answer 1

what is f'`(x) ?

Answer 2

Function f(x)=look above for x>0, and f(x)=0 for x=0

Answer 3

you want to find the constant c on the interval of (0,1) such that f`(c) (the slope of the function at x=c) =0.

you will need to find the 1st derivative.

Answer 4

interval is [0,1]

Answer 5

oh, good:)

Answer 6

what is f`(x) ?

Answer 7

\(\large\color{black}{ \displaystyle f(x)=x\left( {\rm Ln} ~x\right) ^2 }\)
use the product rule for the derivative.

Answer 8

I know. there is Mean value theorem: if function continuous and differentiable on interval, then there is c in that interval (a,b)- (0,1) in my case - such that f'(c) = (f(b)-f(a))/(b-a) (=0 in my case). I need to find c