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Yanka [14]
3 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]3 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. 
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