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Question:

Let f(x) = sin4x + cos4x. Then f is an increasing function in the interval:

[0,π/4]

[π/4,π/2]

[5π/8,3π/4]

[π/2,5π/8]

Solution:

f(x)=sin4x+cos4xf′(x)=4sin3xcosx+4cos3x(−sinx)