Mathematics

Problem

Consider the function

f(x)=x e^{-x^{2}}

. Which option lists the coordinates of the relative maximum and relative minimum of

f

? a) Relative maximum at

\left(-\dfrac{1}{\sqrt{2}},-\dfrac{e^{-1/2}}{\sqrt{2}}\right)

and relative minimum at

\left(\dfrac{1}{\sqrt{2}},\dfrac{e^{-1/2}}{\sqrt{2}}\right)

b) Relative maximum at

\left(\dfrac{1}{\sqrt{2}},\dfrac{e^{-1/2}}{\sqrt{2}}\right)

and relative minimum at

\left(-\dfrac{1}{\sqrt{2}},-\dfrac{e^{-1/2}}{\sqrt{2}}\right)

c) Relative maximum at

\left(\dfrac{1}{2},\dfrac{e^{-1/4}}{2}\right)

and relative minimum at

\left(-\dfrac{1}{2},-\dfrac{e^{-1/4}}{2}\right)

d) Relative maximum at

\left(\dfrac{1}{\sqrt{2}},e^{-1/2}\right)

and relative minimum at

\left(-\dfrac{1}{\sqrt{2}},-e^{-1/2}\right)