Find constants a and b in the function f(x)=axe^(bx)such that f(3/4)=1 and the function has a local maximum at x=3/4.

Question

a=

b=

Answer 1

y = a x e^(bx)
dy/dx = ax [ b e^(bx ] + a e^(bx) = a e^(bx) [ x b + 1]
that is zero at x = 3/4
so (3/4)b + 1 = 0
b = -4/3
y =a x e^-(4x/3)
1 = a (3/4) e^- 1
e = (3/4) a
a = 4 e / 3