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 maxima and local minima, and the corresponding local maximum and local minimum values of the following functions: (i) f(x) = x sqrt(1 - x) , where x gt 0 (ii) f(x) = (x)/((x -1) (x -4)), " where " 1 lt x lt 4

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 all the points of local maxima and local minima as well as the corresponding local maximum and local minimum values for the function f(x)=(x-1)^(3)(x+1)^(2)

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of each of the following functions.Also,find the points of inflection,if any : f(x)=xe^(x)

Find the sum of the local maximum and local minimum values of the function f (x) = (tan 3x)/(tan^(3) x) on interval (0 , pi//2) .

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of each of the following functions.Also,find the points of inflection,if any: f(x)=x^(4)-62x^(2)+120x+9

Let f(x) =x +(1)/(x). find local maximum and local minimum value of f(x) . Can you explain this discrepancy of locally minimum value being greater than locally maximum value.

Find the local maximum and local minimum value of f(x)= x^(3)-3x^(2)-24x+5

Find the points of local maxima and local minima, if any, of the following functions. Find also the local maximum and local minimum values : f(x)=cosx, 0ltxltpi