First derivative test for local maxima and minima (method and how it comes)

To find local maxima or minima

Problems based on local maxima and minima

Find the points of local maxima or local minima, if any, using first derivative test, and local maximum or local minimum of f(x)=sinx-cosx , 0

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of ' f(x)=cos x,110

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=x sqrt(1-x),x>0

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=2sin x-x,-(pi)/(2)<=x<=(pi)/(2)

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)=(x)/(2)+(2)/(x),x>0

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)=sin2x-x,quad -(pi)/(2)<=x<=(pi)/(2)

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^(3)(x-1)^(2)