What is the extreme f(x)=3x^4-8x^3-144x^2+1 ?

The extreme f(x)=3x^4-8x^3-144x^2+1 is Minimum(-4,-1023),Maximum(0,1),Minimum(6,-3023)

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extreme f(x)=3x^4-8x^3-144x^2+1

extreme points

f (x) = 3 x^{4} - 8 x^{3} - 144 x^{2} + 1

Minimum (- 4, - 1023), Maximum (0, 1), Minimum (6, - 3023)

Solution steps

f^{'} (x) = 12 x^{3} - 24 x^{2} - 288 x

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 4

into

3 x^{4} - 8 x^{3} - 144 x^{2} + 1 : - 1023

Minimum (- 4, - 1023)

Plug

x = 0

into

3 x^{4} - 8 x^{3} - 144 x^{2} + 1 : 1

Maximum (0, 1)

Plug

x = 6

into

3 x^{4} - 8 x^{3} - 144 x^{2} + 1 : - 3023

Minimum (6, - 3023)

Minimum (- 4, - 1023), Maximum (0, 1), Minimum (6, - 3023)

f (x, y) = - 5 x^{2} - 5 x y - 7 y^{2} + 50 x - 67 y + 9

y = x^{2} + 2 x + 2

\frac{x ^{2}}{x ^{2} + 2}

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

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

What is the extreme f(x)=3x^4-8x^3-144x^2+1 ?
The extreme f(x)=3x^4-8x^3-144x^2+1 is Minimum(-4,-1023),Maximum(0,1),Minimum(6,-3023)