[tex]y = 2x {}^{2} + e {}^{ - x {}^{4} } [/tex]
[tex] \frac{dy}{dx} = 4x +( e {}^{ - x {}^{4} } )( - 4x {}^{3} )[/tex]
[tex] \frac{dy}{dx} = 4x - 4x {}^{3} e { }^{ - x {}^{4} } [/tex]
[tex] \frac{dy}{dx} = 4x(1 - x {}^{2} e {}^{ - x {}^{4} } )[/tex]
[tex] \frac{dy}{dx} = 0 \\ 4x = 0 \: \: \: \: \: 1 - x {}^{2} e {}^{ - x {}^{4} } = 0[/tex]
[tex]4x = 0 \\ x = 0 \: \: \: \: \: \: y(0) = 0 + e {}^{0} = 1[/tex]
[tex] \frac{x {}^{2} }{e {}^{x {}^{4} } } = 1 \\ x {}^{2} = e {}^{x {}^{4} } \\ 2ln(x) = x {}^{4} \\ these \: 2 \: functions \: do \: not \: intersect[/tex]
Stationary point ( 0 , 1 )
