max ⁡ + min ⁡ \max + \min

Geometry Level 3

sin ⁡ 3 x − sin ⁡ 2 x \large \sin^3 x-\sin^2 x

Find the sum of the maximum and minimum values of the expression above.


The answer is -2.

Aly Ahmed by Aly Ahmed , 34, Egypt

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1 solution

The expression is minimum when sin ⁡ x = − 1 \sin x=-1 , the minimum value being − 2 -2 . Since ∣ sin ⁡ 3 x ∣ ≤ sin ⁡ 2 x |\sin^3 x|\leq \sin^2 x , the maximum value of the expression is 0 0 . So the required sum is − 2 + 0 = − 2 -2+0=\boxed {-2} .

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