What is the critical sqrt(x-3ln(x)) ?

The critical sqrt(x-3ln(x)) is x=-3\W_{0}(-1/3),x=-3\W_{-1}(-1/3)

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critical sqrt(x-3ln(x))

critical points

x - 3 ln (x)

x = - 3 W_{0} (- \frac{1}{3}), x = - 3 W_{- 1} (- \frac{1}{3})

Solution steps

x - 3 ln (x)

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = - 3 W_{0} (- \frac{1}{3}), x = - 3 W_{- 1} (- \frac{1}{3})

Identify critical points not in

f (x)

domain

Domain of

x - 3 ln (x) : 0 < x \leq - 3 W_{0} (- \frac{1}{3}) or x \geq - 3 W_{- 1} (- \frac{1}{3})

x - 3 ln (x)

is not defined at

x = 0

, therefore:

x = - 3 W_{0} (- \frac{1}{3}), x = - 3 W_{- 1} (- \frac{1}{3})

y^{1} = x^{2} - 3 x + 2

f (x) = x^{3} + 12 x^{2} - 27 x + 3

f (x) = - 2 x^{3} + 36 x^{2} - 162 x + 6

f (x) = 2 x^{3} + 3 x^{2} + 12 x - 4

f (x) = 2 x^{3} - 3 x^{2} y - 12 x^{2} - 3 y^{2}

What is the critical sqrt(x-3ln(x)) ?
The critical sqrt(x-3ln(x)) is x=-3\W_{0}(-1/3),x=-3\W_{-1}(-1/3)