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I was reading a math book that says that the function below is less or equal to 3. Why is that?

\[ \Large 2^{\sin^2 x} + \dfrac2{2^{\sin^2 x}} \]

Note by Yossi Levi
8 months, 2 weeks ago

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Let \( \large f(x) = 2^{\sin^2 x} + \dfrac{2}{2^{\sin^2 x}} \)

\( \large \Rightarrow 2^{\sin^2 x}+2^{\cos^2 x} \)

which has a maximum value of \( 3\), equality at \( x=\frac{\pi}{2} + n\pi \) or \( x = n\pi \)

where \( n \) is a whole number.

Rahil Sehgal - 8 months, 2 weeks ago

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