Consider on the interval

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider f(x)=sin⁡x+cos⁡xf(x)=\sin x+\cos x on the interval [0,2π][0,2\pi]. On which of the following intervals is ff increasing? (a) (π4,5π4)(\dfrac{\pi}{4},\dfrac{5\pi}{4}) (b) (0,3π4) and (7π4,2π)(0,\dfrac{3\pi}{4})\text{ and }(\dfrac{7\pi}{4},2\pi) (c) (0,π4) and (5π4,2π)(0,\dfrac{\pi}{4})\text{ and }(\dfrac{5\pi}{4},2\pi) (d) (0,π4)(0,\dfrac{\pi}{4})

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