Question:medium
Let $f(x) = \sin x \sin(x + \frac{\pi}{3}), x \in \mathbb{R}$. Then the minimum value of $f$ is equal to
Let $f(x) = \sin x \sin(x + \frac{\pi}{3}), x \in \mathbb{R}$. Then the minimum value of $f$ is equal to
Show Hint
Any function of the form \( a + b \cos \theta \) has a minimum value of \( a - |b| \). Transforming products into sums makes this property immediately applicable.
Updated On: Jun 24, 2026
- $\frac{1}{4}$
- $\frac{-1}{4}$
- $\frac{3}{4}$
- $\frac{-3}{4}$
- $\frac{3}{2}$
Show Solution
The Correct Option is B
Solution and Explanation
Was this answer helpful?
0
Top Questions on Maxima and Minima
Define \( f(x) = \begin{cases} x^2 + bx + c, & x< 1 \\ x, & x \geq 1 \end{cases} \). If f(x) is differentiable at x=1, then b−c is equal to
- MHT CET - 2024
- Mathematics
- Maxima and Minima
- The maximum value of the function \( f(x) = -2x^2 + 4x + 1 \) occurs at:
- MHT CET - 2025
- Mathematics
- Maxima and Minima
- Let $ f(x) = |x^2 - 4x + 3| + |x^2 - 5x + 6| $. The minimum value of $ f(x) $ is:
- BITSAT - 2025
- Mathematics
- Maxima and Minima
- Determine the number of units (\( x \)) that should be sold to maximise the revenue \( R(x) = x \cdot p(x) \). Also verify the result.
- CBSE Class XII - 2024
- Mathematics
- Maxima and Minima
- Want to practice more? Try solving extra ecology questions todayView All Questions
