Question

what can be the highest value of sin^3x+cos^3x

plz give proper explaination.


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Answer 1

Answer:

y = sin3 x + cos3 x

dy / dx = 3 sin2x cosx – 3 cos2x sinx

= 3 sinx cosx (sinx – cosx)

Put dy / dx = 0

3 sinx cosx (sinx – cosx) = 0

x = 0, π / 2, π / 4

y has maximum value at x = 0 or π / 2.

ymax = 1

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