What is the extreme f(x)=3x^4-216x^2-5 ?

The extreme f(x)=3x^4-216x^2-5 is Minimum(-6,-3893),Maximum(0,-5),Minimum(6,-3893)

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extreme f(x)=3x^4-216x^2-5

extreme points

f (x) = 3 x^{4} - 216 x^{2} - 5

Minimum (- 6, - 3893), Maximum (0, - 5), Minimum (6, - 3893)

Solution steps

f^{'} (x) = 12 x^{3} - 432 x

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 6

into

3 x^{4} - 216 x^{2} - 5 : - 3893

Minimum (- 6, - 3893)

Plug

x = 0

into

3 x^{4} - 216 x^{2} - 5 : - 5

Maximum (0, - 5)

Plug

x = 6

into

3 x^{4} - 216 x^{2} - 5 : - 3893

Minimum (6, - 3893)

Minimum (- 6, - 3893), Maximum (0, - 5), Minimum (6, - 3893)

f (x) = x (16 - 39 + 2 x) (\frac{39}{2} - x)

6 x - 7 x^{\frac{6}{7}}

f (x) = - x^{\frac{2}{3}} (x - 5), - 5 \leq x \leq 5

f (x, y) = \frac{x ^{3}}{3} - \frac{y ^{3}}{3} + 2 x y

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

What is the extreme f(x)=3x^4-216x^2-5 ?
The extreme f(x)=3x^4-216x^2-5 is Minimum(-6,-3893),Maximum(0,-5),Minimum(6,-3893)