Application of Derivatives
Maxima and Minima
JEE Main 2021
Grade 12
Question:
The maximum value of $f(x) = \sin x + \cos x$ on $\left[0, \frac{\pi}{2}\right]$ is:
(1) $1$
(2) $\sqrt{2}$
(3) $2$
(4) $\frac{1}{\sqrt{2}}$
Step-by-Step Solution
Key Concept: Rewrite $f(x)$ in the single-term form $R \sin(x + \alpha)$ — its maximum value can then be read off directly without further differentiation.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)