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if the function f(x) = x^(3)+3(a-7)x^(2)+3(a^(2)-9)x -1 has a positive point of maximum, then a belongs to what values in Real numbers

if the function f(x) = x^(3)+3(a-7)x^(2)+3(a^(2)-9)x -1 has a positive point of maximum, then


a belongs to what values in Real numbers

Grade:

1 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

df(x)/dx = 3x^2 +6(a-7)x +3(a^2 -9)=0, solving the quadratic equation in x and then simplifying, we get

x= 7-a±√(58-14a) thus firstly 58>14a,a<29/7 , d2f(x)/dx2= 6x+6(a-7)<0,7-a>x, 7-a>x±√(58-14a), 7-a=x+√(58-14a),

x=7-a-√(58-14a)>0 implies a2>9. Also, we have the earlier result a<29/7, therefore a<-3 or +3<a<29/7

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