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increasing/decreasing function

Source: LIMIT 2019 CBS1 P8

April 28, 2021
function

Problem Statement

If f(x)=cos⁡(x)−1+x22f(x)=\cos(x)-1+\frac{x^2}2, then <spanclass=′latex−bold′>(A)</span> f(x) is an increasing function on the real line<span class='latex-bold'>(A)</span>~f(x)\text{ is an increasing function on the real line} <spanclass=′latex−bold′>(B)</span> f(x) is a decreasing function on the real line<span class='latex-bold'>(B)</span>~f(x)\text{ is a decreasing function on the real line} <spanclass=′latex−bold′>(C)</span> f(x) is increasing on −∞<x≤0 and decreasing on 0≤x<∞<span class='latex-bold'>(C)</span>~f(x)\text{ is increasing on }-\infty<x\le0\text{ and decreasing on }0\le x<\infty <spanclass=′latex−bold′>(D)</span> f(x) is decreasing on −∞<x≤0 and increasing on 0≤x<∞<span class='latex-bold'>(D)</span>~f(x)\text{ is decreasing on }-\infty<x\le0\text{ and increasing on }0\le x<\infty
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