Question

how to find minimum and maximum values for ncosx+msinx

Answer 1

Answer
For maximum or minimum value of any function first find the derivative of it

Let y=Sinx +Cosx

d/dx(sin x+cos x)

dy/dx=cosx -sinx

For maximum/minimum value

dy/dx =0

Cos x -Sin x=0

Cosx =Sinx

Or tanx =1

Or x =tan inverse (1)

x =π/4

For finding whether the function will have minimum or maximum value at x =π/4 ,we should find the second derivative

Y 2 =-Sinx -Cosx

Or Y 2=-1(Sin x+Cos x)

As the Second Derivative (Y2) is negative so the function has maxima at π/4