jee-main 2015 Q72

jee-main · India · 10apr Stationary points and optimisation Determine parameters from given extremum conditions

Let $f: \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = \begin{cases} k - 2x, & \text{if } x \leq -1 \\ 2x + 3, & \text{if } x > -1 \end{cases}$. If $f$ has a local minimum at $x = -1$, then a possible value of $k$ is:
(1) $0$
(2) $-\frac{1}{2}$
(3) $-1$
(4) $1$

Let $f: \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = \begin{cases} k - 2x, & \text{if } x \leq -1 \\ 2x + 3, & \text{if } x > -1 \end{cases}$. If $f$ has a local minimum at $x = -1$, then a possible value of $k$ is:\\
(1) $0$\\
(2) $-\frac{1}{2}$\\
(3) $-1$\\
(4) $1$

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