What is the extreme f(x)=3x^4-54x^2+2 ?

The extreme f(x)=3x^4-54x^2+2 is Minimum(-3,-241),Maximum(0,2),Minimum(3,-241)

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extreme f(x)=3x^4-54x^2+2

extreme points

f (x) = 3 x^{4} - 54 x^{2} + 2

Minimum (- 3, - 241), Maximum (0, 2), Minimum (3, - 241)

Solution steps

f^{'} (x) = 12 x^{3} - 108 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

3 x^{4} - 54 x^{2} + 2 : - 241

Minimum (- 3, - 241)

Plug

x = 0

into

3 x^{4} - 54 x^{2} + 2 : 2

Maximum (0, 2)

Plug

x = 3

into

3 x^{4} - 54 x^{2} + 2 : - 241

Minimum (3, - 241)

Minimum (- 3, - 241), Maximum (0, 2), Minimum (3, - 241)

f (x) = \frac{lo g _{10} ( x )}{x}

f (x) = t^{2} - 6 t + 8

P (x, y) = 3 x + 4 y

f (1) = x + 3

f (x) = - \frac{5}{12} x^{3} - 5 x^{2} - 15 x - 6

What is the extreme f(x)=3x^4-54x^2+2 ?
The extreme f(x)=3x^4-54x^2+2 is Minimum(-3,-241),Maximum(0,2),Minimum(3,-241)