i7nd4JayBntbabygirl i7nd4JayBntbabygirl

15-08-2016
Mathematics

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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?

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HomertheGenius HomertheGenius

18-08-2016

g `( x ) =[tex] 2x * e^{kx} + k x^{2} *e^{kx} = \\ = xe^{kx}(2 + kx ) [/tex]
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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