Consider the function

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider the function f(x)=xe−x2f(x)=x e^{-x^{2}}. Which option lists the coordinates of the relative maximum and relative minimum of ff? (a) Relative maximum at (−12,−e−1/22)\left(-\dfrac{1}{\sqrt{2}},-\dfrac{e^{-1/2}}{\sqrt{2}}\right) and relative minimum at (12,e−1/22)\left(\dfrac{1}{\sqrt{2}},\dfrac{e^{-1/2}}{\sqrt{2}}\right) (b) Relative maximum at (12,e−1/22)\left(\dfrac{1}{\sqrt{2}},\dfrac{e^{-1/2}}{\sqrt{2}}\right) and relative minimum at (−12,−e−1/22)\left(-\dfrac{1}{\sqrt{2}},-\dfrac{e^{-1/2}}{\sqrt{2}}\right) (c) Relative maximum at (12,e−1/42)\left(\dfrac{1}{2},\dfrac{e^{-1/4}}{2}\right) and relative minimum at (−12,−e−1/42)\left(-\dfrac{1}{2},-\dfrac{e^{-1/4}}{2}\right) (d) Relative maximum at (12,e−1/2)\left(\dfrac{1}{\sqrt{2}},e^{-1/2}\right) and relative minimum at (−12,−e−1/2)\left(-\dfrac{1}{\sqrt{2}},-e^{-1/2}\right)

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