Question

Let a function f(x) be defined as

f(x) =$\left\{ \begin{matrix} \sin^{- 1}\lambda + x^{2}; & 0 < x < 1 \\ & \\ 2x; & x \geq 1 \end{matrix} \right.\$

f(x) can have local minimum at x = 1 if the value of l lies in the interval –

• A. [sin 1, 1]
• B. (– sin 1, 1)
• C. (sin 1, 1]
• D. [0, sin 1]

Answer 1

Answer: (C)

(sin 1, 1]

Answer 2

For local minimum at x = 1, the graph should be

Hence 1 + sin^–1 l > 2

̃ sin^–1 l > 1

̃ l Î (sin 1, 1]