What are the critical points of f(x)=x^2+(k/x)?
I’m getting the answer 3 square root 4k/2 but I don’t know if that’s right
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answers:
MyRank say: f(x) = x² + (k/x)

f’(x) = 2x – k/x²

f’(x) = 0

2x – k/x² = 0

2x = k/x²

2x³ = k

x³ = k/2

x = 3√k/2 substitute given that

y = (3√k/2)² + (k/x)

(x, y) = ((k/2)¹/³, (k/2)¹/³ + k(k/2)⁻¹/³).
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alex say: f'(x) = 2x - k/x^2 = 0 --->x = (k/2)^(1/3)
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rotchm say: Taking 'critical points' as to mean there where the derivative is zero.


f(x)=x^2+(k/x)

What is the derivative of that? Hint: the two terms here are of the form xⁿ, and you know the derivative.

Show your steps here & we can proceed if need be. ]

Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them.
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Captain Matticus, LandPiratesInc say: f(x) = x^2 + k * x^(-1)
f'(x) = 2x - k * x^(-2)
f'(x) = 0
0 = 2x - k / x^2
k / x^2 = 2x
k = 2x^3
k/2 = x^3
(k/2)^(1/3) = x
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dxjlb say: inohadiq
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iulgi say: jklzkjen
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