contestada

Let g be the function given by g(x)=x2ekx, where k is a constant. For what value of k does g have a critical point at x=23?.

Respuesta :

LammettHash

It looks like we have

[tex]g(x) = x^2 e^{kx}[/tex]

If x = 23 is a critical point of g(x), then

[tex]g'(x) = 2x e^{kx} + kx^2 e^{kx} = (kx^2 + 2x) e^{kx}[/tex]

[tex]\implies g'(23) = (23^2k + 46) e^{23k} = 0[/tex]

[tex]e^{23k}[/tex] is positive for all k, so we're left with

23² k + 46 = 0

23² k = -46

k = -46/23²

k = -2/23