f (x) = \(a x e^{b x^{2} }\)
f (x) = \(a( e^{b x^{2} } +x e ^{b x^{2} } *2 b x )=a e ^{b x^{2} } (1+2b x^{2} )\)
f ( 1 ) = 4
f ( 1 ) = 0
\(4 = a e ^{b} \\ a e ^{b} (1 + 2 b ) = 0 \\ 4 ( 1 + 2 b )= 0\)
b = -1/2
\(4=a e ^{-1/2} = \frac{a}{ \sqrt{e} } \\ a = 4 \sqrt{e}\)
Answer: a = 4√e, b = -1/2
