For what value of `x`, `x^2ln(1/x)` is maximum

For what value of x will (x-1)(3-x) have its maximum ?

Show that the function (-x^(2) log x) is maximum at x= 1/sqrte .

For what values of x, the expression 2x - 7 - 5x ^(2) is maximum and also find the maximum value.

Find for what values of x the following functions are maximum and minimum Also find the corresponding maximum and minimum values : (1)/(2)x^(4)-2x^(3)-6x^(2)+16x+1

The maximum value of (log x)/( x) is

The maximum value of (ln x)/x is