# Calculus

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Find constants a and b in the function f(x)=axe^(bX) such that f(1/8)=1 and the function has a local maximum at x=1/8.

• Calculus -

f = ax e^(bx)
f' = ae^(bx) + abx e^(bx)
= ae^(bx) (1+bx)

f'(1/8) = 0, so b = -8
f(1/8) = 1 = a(1/8)e^(-1), so a=8e

f(x) = (8e)x e^(-8x)

• Calculus -

Calculus - Steve, Wednesday, March 6, 2013 at 5:00pm

f = ax e^(bx)
f' = ae^(bx) + abx e^(bx)
= ae^(bx) (1+bx)

f'(1/8) = 0, so b = -8
f(1/8) = 1 = a(1/8)e^(-1), so a=8e

f(x) = (8e)x e^(-8x)

• Calculus -

you suck steve

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