The set of all the possible values of ‘a’ for whi

Question

The set of all the possible values of ‘a’ for which the function f(x)=5+(a-2)x+(a-1)x^2-x^3 has a local minimum values at some x1

Vikas TU · Accepted Answer

Dear Student,f(x) = 5 + (a-2)x + (a-1)x2 – x3.The extremum occurs when f'(x) = (a-2) + 2(a-1)x – 3x2 = 0.For x1, the condition for extremum is 3x12 - 2(a-1)x1 – (a-2) = 0.For this x1 to be minimum, f''(x1) gretare than equals 0.6x1 – 2(a-1) ≥ 0 => 6x1 ≥ 2(a-1) => 3x1 ≥ a-1 => 3x1 + 1 ≥ a.Henc ethe possible values of a would be in term of x =>a less than equalls to all the values 3x1 + 1.Cheers!!Regards,Vikas (B. Tech. 4th yearThapar University)

Differential Calculus> The set of all the possible values of ‘a’...

The set of all the possible values of ‘a’ for which the function f(x)=5+(a-2)x+(a-1)x^2-x^3 has a local minimum values at some x1

utkarsh ambasta , 7 Years ago

Vikas TU

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differential calculus

Differential Calculus> The set of all the possible values of ‘a’...

The set of all the possible values of ‘a’ for which the function f(x)=5+(a-2)x+(a-1)x^2-x^3 has a local minimum values at some x1

utkarsh ambasta , 7 Years ago

Vikas TU

LIVE ONLINE CLASSES

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