What is the extreme f(x)=2x^3-3ax^2+a^3 ?

The extreme f(x)=2x^3-3ax^2+a^3 is {a 0: Maximum(0,a^3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=2x^3-3ax^2+a^3

extreme points

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

{a < 0 : Minimum (0, a^{3}), a > 0 : Maximum (0, a^{3})}

Solution steps

Find the critical points:

x = 0, x = a

f^{''} (x) = 12 x - 6 a

Check the sign of

f^{''} (x) = 12 x - 6 a

at each critical point

Check critical point

x = 0 : {a < 0 : Minimum (0, a^{3}), a > 0 : Maximum (0, a^{3})}

{a < 0 : Minimum (0, a^{3}), a > 0 : Maximum (0, a^{3})}

What is the extreme f(x)=2x^3-3ax^2+a^3 ?
The extreme f(x)=2x^3-3ax^2+a^3 is {a<0: Minimum(0,a^3),a>0: Maximum(0,a^3)}