Local maximum and local minimum and condition for it

Find the points of local maxima and local minima, if any, of the following functions. Find also the local maximum and local minimum values : The constant function alpha .

Find the local maximum and local minimum value (if any) of the function y=x^3-27x+5

Find the points of local maximum and local minimum, if any, of the function: f(x)=sin x- cos x, 0 < x < 2pi . Also find the local maximum and local minimum values.

Find the points of local maxima and local minima,if any,and local maximum and local minimum values of f(x)=s in^(4)x+cos^(4)x

Find the local maximum and local minimum of the function x^(4) - 3x^(3) + 3x^(2) -x

Find the local maximum and local minimum values of the function f(x) = (4)/(x + 2) + x .