What is the extreme f(x)=3x^4+4x^3-12x^2+10 ?

The extreme f(x)=3x^4+4x^3-12x^2+10 is Minimum(-2,-22),Maximum(0,10),Minimum(1,5)

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extreme f(x)=3x^4+4x^3-12x^2+10

extreme points

f (x) = 3 x^{4} + 4 x^{3} - 12 x^{2} + 10

Minimum (- 2, - 22), Maximum (0, 10), Minimum (1, 5)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

3 x^{4} + 4 x^{3} - 12 x^{2} + 10 : - 22

Minimum (- 2, - 22)

Plug

x = 0

into

3 x^{4} + 4 x^{3} - 12 x^{2} + 10 : 10

Maximum (0, 10)

Plug

x = 1

into

3 x^{4} + 4 x^{3} - 12 x^{2} + 10 : 5

Minimum (1, 5)

Minimum (- 2, - 22), Maximum (0, 10), Minimum (1, 5)

x 4 - x

f (x) = x^{2} + 8 x + 19

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

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

f (x) = x^{2} + x y + y^{2}

What is the extreme f(x)=3x^4+4x^3-12x^2+10 ?
The extreme f(x)=3x^4+4x^3-12x^2+10 is Minimum(-2,-22),Maximum(0,10),Minimum(1,5)