Find the local extrema for the following functions using second derivative test :
`f(x)=xlogx`

Find the local extrema for the following functions using second derivative test : f(x)=x^(2)e^(-2x)

Find the local extrema for the following functions using second derivative test : f(x)=-3x^(5)+5x^(3)

Find the second derivative of the following functions: x^x

Find the points of local maxima or local minima, if any, of the following function, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be: f(x)=(x-5)^4

Find the points of local maxima or local minima, if any, of the following function, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be: f(x)=cosx ,0

Find the local extrema of the function f(x)=4x^(6)-6x^(4)

Find the points of local extrema for the function f(x) = sinx on [0,4pi]

Find the points of local maxima or local minima, if any, of the following function, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be: f(x)=x/2+2/x ,x >0