TS EAMCET · Maths · Application of Derivatives
The maximum value of the function \(f(x)=3 \sin ^{12} x+\) \(4 \cos ^{16} x\) is
- A 4
- B 5
- C 6
- D 7
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
\(f(x)=3 \sin ^{12} x+4 \cos ^{16} x\) Maximum value of \(\sin ^{12} x\) and \(\cos ^{16} x\) is 1 and minimum value is 0 . \(\therefore\) Value of \(f(x)\) is maximum when \(\sin ^{12} x=0\) and \(\cos ^{16} x=1\). \(\therefore\) Maximum value of \(f(x)=4\).
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