Question:
Let \( f(x) = (3\sin^2(10x+11) - 7)^2 \) for \( x \in \mathbb{R} \). Then the maximum value of the function is
Let \( f(x) = (3\sin^2(10x+11) - 7)^2 \) for \( x \in \mathbb{R} \). Then the maximum value of the function is
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For squared expressions, check extreme values of inner expression.
Updated On: May 8, 2026
- \( 9 \)
- \( 16 \)
- \( 49 \)
- \( 100 \)
- \( 121 \)
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The Correct Option is C
Solution and Explanation
Concept:
\[
0 \le \sin^2\theta \le 1
\]
Step 1: Range
\[ 0 \le 3\sin^2\theta \le 3 \] \[ -7 \le 3\sin^2\theta -7 \le -4 \]
Step 2: Square
\[ (3\sin^2\theta -7)^2 \] Maximum occurs at extreme: \[ (-7)^2 = 49 \] \[ (-4)^2 = 16 \] Thus maximum: \[ \boxed{49} \]
Step 1: Range
\[ 0 \le 3\sin^2\theta \le 3 \] \[ -7 \le 3\sin^2\theta -7 \le -4 \]
Step 2: Square
\[ (3\sin^2\theta -7)^2 \] Maximum occurs at extreme: \[ (-7)^2 = 49 \] \[ (-4)^2 = 16 \] Thus maximum: \[ \boxed{49} \]
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