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Question: The function f(x) = <img src="https://cdn.pureessence.tech/canvas_600.png?top_left_x=0&top_left_y=30...

The function f(x) = has no extrema. if (n Ī z)

A

a – b¹ np

B

b – a = np

C

b – a = 2np

D

) None

Answer

a – b¹ np

Explanation

Solution

f(x) =

Ž f ¢(x)=sin⁡(x+β)cos⁡(x+α)−sin⁡(x+α)cos⁡(x+β)sin⁡2(x+β)\frac { \sin ( x + \beta ) \cos ( x + \alpha ) - \sin ( x + \alpha ) \cos ( x + \beta ) } { \sin ^ { 2 } ( x + \beta ) }

= sin⁡(β−α)sin⁡2(x+β)\frac { \sin ( \beta - \alpha ) } { \sin ^ { 2 } ( x + \beta ) }

\ f(x) has no extreme if f ¢(x) ¹ 0

i.e. sin (b – a) ¹ 0 Ž b – a ¹ n p

or a – b ¹ np