What is the critical f(x)=(x^2)/2-6ln(x)+x ?

The critical f(x)=(x^2)/2-6ln(x)+x is x=2

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critical f(x)=(x^2)/2-6ln(x)+x

critical points

f (x) = \frac{x ^{2}}{2} - 6 ln (x) + x

x = 2

Solution steps

\frac{x ^{2}}{2} - 6 ln (x) + x

Find where

f^{'} (x)

is equal to zero or undefined

x = - 3, x = 2, x = 0

Identify critical points not in

f (x)

domain

Domain of

\frac{x ^{2}}{2} - 6 ln (x) + x : x > 0

\frac{x ^{2}}{2} - 6 ln (x) + x

is not defined at

x = - 3, x = 0

, therefore:

x = 2

3 x^{2} - 18 x + 24

y = x + \frac{1}{x ^{2}}

f (x) = - 2 x^{3} - 18 x^{2} + 42 x + 150

f (x) = x^{5} e^{- 9 x}

What is the critical f(x)=(x^2)/2-6ln(x)+x ?
The critical f(x)=(x^2)/2-6ln(x)+x is x=2