Verified Answer :

HomertheGenius

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. 

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