Show : `4^(x)-8xlog_(e)2` is minimum at x=1

Examine the following functions for maxima and minima : Show that f(x)=x^(x) is minimum when x=(1)/(e) .

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

Show that f(x)=(logx)/x has minimum value at x=e

Show that the value of x^(x) is minimum when x=(1)/(e)

e^x.log (sin 2 x)

If f(x)=|(2^(-x),e^(xlog_(2)2),x^(2)),(2^(-3x),e^(3xlog_(e)2),x^(4)),(2^(-5x),e^(5xlog_(e)2),1)| , then a) f(x) + f(-x) = 0 b)f(x) - f(-x) =0 c)f(x) + f(-x)=2 d)None of these

f(x)=|xlog_(e )x| monotonically decreases in

The integrating factor of the differential equation 3xlog_(e)x(dy)/(dx)+y=2log_(e)x is given by -

If g(x)=|[a^(-x), e^(xlog_e a), x^2] , [a^(-3x), e^(3xlog_e a), x^4] , [a^(-5x), e^(5xlog_e a), 1]| then 1)g(x)+g(-x)=0 2)g(x)-g(-x)=0 3)g(x).g(-x)=0 4)None of these