Question

Find the intervals of increase and decrease of xcos(x)

Answer 1

Answer:

Let take a function f(x)=sinx-cosx.

Differentiate this function and put the zero.

So cosx+sinx=0

So tanx=-1

So x=-π/4,3π/4

At x=-π/4 function has minimum value -√2&x=3π/4 function has maximum value +√2.

So we can say that function is increasing in the interval of -π/4 to 3π/4. Then decreasing in the interval of 3π/4 to 7π/4 this cycle is repeating.

So we can say that the given function is increasing in the interval {-π/4+2nπ,3π/4+2nπ}

Decreasing in the interval{3π/4+2nπ,7π/4+2nπ}

Where n=0,1,2,3……..

Answer 2

Let take a function f(x)=sinx-cosx.

Differentiate this function and put the zero.

So cosx+sinx=0

So tanx=-1

So x=-π/4,3π/4

At x=-π/4 function has minimum value -√2&x=3π/4 function has maximum value +√2.

So we can say that function is increasing in the interval of -π/4 to 3π/4. Then decreasing in the interval of 3π/4 to 7π/4 this cycle is repeating.

So we can say that the given function is increasing in the interval {-π/4+2nπ,3π/4+2nπ}

Decreasing in the interval{3π/4+2nπ,7π/4+2nπ}

Where n=0,1,2,3