Question

Find whether f(x)=cos(2x+π/4)isincreasingordecreasingin(3π8,5π8) .

Answer 1

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Answer 2

Answer:

f(x)= cos (2x+π/4)

f'x= -2sin (2x+π/4)

this lies between 3π/8 < x < 5π/8

(3π/8) 2< 2x < (5π/8) 2(multiplied by 2)

3π/4 < 2x < 5π/4

3π/4+π/4 < 2x+π/4 < 5π/4+π/4( add π/4)

π < 2x+π/4 < 3π/2

ie, 3rd quadrant

so sin 2x+π/4 is negative

dy/dx is positive

hence f(x) is increasing in the given interval.