IIT-JEE Advanced 2022 Maths Paper 2 Problem 10

Problem

Let α = \( \sum_{k=1}^{\infty} \) sin^2k(π/6). Let g: [0, 1] → R be the function defined by g(x) = 2^αx + 2^{α(1 − x)}. Then, which of the following statements is/are true?

A The minimum value of g(x) is 2^7/6.
B The maximum value of g(x) is 1 + 2^1/3.
C The function g(x) attains its maximum at more than one point.
D The function g(x) attains its minimum at more than one point.

Solution

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