Find the interval in which the/f is given byfx sinx+ cosx 0
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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……..
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……..
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