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NDA Math Application of Derivatives

For the next two items that follow :

Consider the function

f(x)=\left|x-1\right|+x^{2}

where

x\in\mathbb{R}

[NDA I 2016]

Question : 52 of 73

Marks: +1, -0

Solution:

f(x)

has local minimum at one point only

(-\infty,\infty)

f'(x)=\begin{cases}2x-1 & \text{; } x < 1 \\ 2x+1 & \text{; } x \ge 1 \end{cases}

Clearly, for

(x>1);f'(x)>0 \ge \&\;\text{for}\;(x<1)

x=\frac{1}{2}

is the point of local minima

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