Define local maxima and local minima (or) What is second derivative test?

To find local maxima or 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)=(x-5)^4

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)=x^3-3x

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^3(x-1)^2

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-1)(x+2)^2

Find the points of local maxima or local minima, if any, using first derivative test, and local maximum or local minimum of f(x)=1/(x^2+2)

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^3-6x^2+9x+15

Find the points of local maxima or local minima, if any, using first derivative test, and local maximum or local minimum of f(x)=sin2x , 0ltxltpi

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 , x in (0, 2 pi)