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extrema of |x^2-1|

Source: LIMIT 2019 CBS2 P9

April 28, 2021
algebra

Problem Statement

Let f:R→Rf:\mathbb R\to\mathbb R be given by f(x)=∣x2−1∣,x∈Rf(x)=\left|x^2-1\right|,x\in\mathbb RThen <spanclass=′latex−bold′>(A)</span> f has local minima at x=±1 but no local maxima<span class='latex-bold'>(A)</span>~f\text{ has local minima at }x=\pm1\text{ but no local maxima} <spanclass=′latex−bold′>(B)</span> f has a local maximum at x=0 but no local minima<span class='latex-bold'>(B)</span>~f\text{ has a local maximum at }x=0\text{ but no local minima} <spanclass=′latex−bold′>(C)</span> f has local minima at x=±1 and a local maximum at x=0<span class='latex-bold'>(C)</span>~f\text{ has local minima at }x=\pm1\text{ and a local maximum at }x=0 <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
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