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

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

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

extreme points

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

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

Solution steps

Find the critical points:

x = 0, x = \frac{2 a}{3}

f^{''} (x) = 6 x - 2 a

Check the sign of

f^{''} (x) = 6 x - 2 a

at each critical point

Check critical point

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

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

f (x) = 3 x^{2} + 4 y^{3} - 12 x y + 37

f (x) = 15 x + 18 y - 2 x^{2} + 2 x y + 3 y^{2}

f (x, y) = x^{3} - 12 x + y^{2} + 6 y + 14

f (x) = x^{- 7} ln (x)

f (x, y) = y (e^{x} - 1)

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