What is the critical f(x)=12x^3+12x^2-24x ?

The critical f(x)=12x^3+12x^2-24x is x=-(1+sqrt(7))/3 ,x=(-1+sqrt(7))/3

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critical f(x)=12x^3+12x^2-24x

critical points

f (x) = 12 x^{3} + 12 x^{2} - 24 x

x = - \frac{1 + 7}{3}, x = \frac{- 1 + 7}{3}

Solution steps

12 x^{3} + 12 x^{2} - 24 x

Find where

f^{'} (x)

is equal to zero or undefined

x = - \frac{1 + 7}{3}, x = \frac{- 1 + 7}{3}

Identify critical points not in

f (x)

domain

Domain of

12 x^{3} + 12 x^{2} - 24 x : - \infty < x < \infty

All critical points are in domain

x = - \frac{1 + 7}{3}, x = \frac{- 1 + 7}{3}

f (x) = 1 - 6 x

f (x) = 3 x^{4} + 7

x e^{\frac{1}{x}}

\frac{45 π}{4}

What is the critical f(x)=12x^3+12x^2-24x ?
The critical f(x)=12x^3+12x^2-24x is x=-(1+sqrt(7))/3 ,x=(-1+sqrt(7))/3