Let $f(x)=\left\{\begin{array}{l}|x

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

Let $f(x)=\left\{\begin{array}{l}|x-1|+a, x<1 \\ 2 x+3, x \geq 1\end{array}\right.$. If f (x) has a local minima at x = 1, then

Options:

a ≥ 5

a > 5

a > 0

none of these

Correct Answer:

a ≥ 5

Explanation:

Local minimum value of f(x) at x = 1, will be 5

i.e. 1 – x + a ≥ 5 at x = 1 ⇒ a ≥ 5