Let g be the function given by g(x)=x^2*e^(kx) , where k is a constant. For what value of k does g have a critical point at x=2/

Question

Yanka [14]

2 years ago

8

Let g be the function given by g(x)=x^2*e^(kx) , where k is a constant. For what value of k does g have a critical point at x=2/

3?

Mathematics

1 answer:

ArbitrLikvidat [17] · Answer 1 · 2022-03-23T04:31:57+03:00

ArbitrLikvidat [17]2 years ago

8 0

G `( x ) = $2x * e^{kx} + k x^{2} *e^{kx} = \\ = xe^{kx}(2 + kx )$
2 + k x = 0
k x = -2
k = -2: x = - 2 : 2/3 = - 2 * 3/2
k = - 3
Answer: for k= - 3, the function g ( x ) have a critical point at x = 2/3.