What is the extreme f(x)=4x^4-2a^2x^3 ?

The extreme f(x)=4x^4-2a^2x^3 is Inconclusive(0,0)

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extreme f(x)=4x^4-2a^2x^3

extreme points

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

Inconclusive (0, 0)

Solution steps

Find the critical points:

x = 0, x = \frac{3 a ^{2}}{8}

f^{''} (x) = 48 x^{2} - 12 a^{2} x

Check the sign of

f^{''} (x) = 48 x^{2} - 12 a^{2} x

at each critical point

Check critical point

x = 0 :

Inconclusive

Since

x = 0

, the second derivative test is inconclusive

Inconclusive

f (x) = x^{4} + 4 x^{3} - 20 x^{2} + 1

f (x) = e^{\frac{x}{2}} (x + y^{2})

f (x) = x^{4} - 50 x^{2} + 1

f (x) = x^{4} - 50 x^{2} + 2

y = x^{3} - 3 x^{2} + 5

What is the extreme f(x)=4x^4-2a^2x^3 ?
The extreme f(x)=4x^4-2a^2x^3 is Inconclusive(0,0)