Let \alpha=\sum_{k=1}^{\infty} \sin ^{2 k}(\frac{\pi}{6}) Let g:[0,1] \to \mathbb{R} be the function defined by g(x)=2^{\alpha x}+2^{\alpha(1-x)} Then, which of the following statements is/are TRUE ? [JEE Adv 2022 P2]

The minimum value of g(x) is 2^{\frac{7}{6}}

The maximum value of g(x) is 1+2^{\frac{1}{3}}

The function g(x) attains its maximum at more than one point

The function g(x) attains its minimum at more than one point

Application of Derivatives

Section: Mathematics

Question : 3 of 32

Marks: +1, -0

Let
α=

∞

∑

k=1

sin2k(‌

)
Let g:[0,1]→ℝ be the function defined by
g(x)=2αx+2α(1−x)
Then, which of the following statements is/are TRUE ?

[JEE Adv 2022 P2]

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