UPSC NDA I 2016 Mathematics Solved Paper

Concept:The function $f(x)$ is decreasing when its graph slopes downward and increasing when it slopes upward.Explanation:From the graph of $f(x)$, observe that the curve falls (decreases) for all $x$ values less than $\frac{1}{2}$.After $x = \frac{1}{2}$, the curve rises (increases) continuously.Thus, $f(x)$ is decreasing in the interval $\left(-\infty, \frac{1}{2}\right)$ and increasing in $\left(\frac{1}{2}, \infty\right)$.Answer:Option B: $f(x)$ is decreasing in $\left(-\infty, \frac{1}{2}\right)$ and increasing in $\left(\frac{1}{2}, \infty\right)$.