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Virty [35]
4 years ago
8

For what values of the numbers a and b does the function below have maximum value f(1) = 4? (Round the answers to three decimal

places.). f(x) = axe^[b(x^2)].
Mathematics
1 answer:
Georgia [21]4 years ago
4 0
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

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