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Application of Derivatives question

2022 · Shift 2 · Q28

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PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2022 · Shift 2 · Q28

Application of Derivatives question

2022 · Shift 2 · Q28

JEE AdvancedMathematicsApplication of DerivativesMultiple correct+4 / −2

Let

\alpha=\sum\limits_{k = 1}^\infty {{{\sin }^{2k}}\left( {{\pi \over 6}} \right)}

Let

g:[0,1] \rightarrow \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 ?

A
The minimum value of $g(x)$ is $2^{\frac{7}{6}}$
B
The maximum value of $g(x)$ is $1+2^{\frac{1}{3}}$
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

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