What is the extreme f(x)=2x^4+16x^3+27 ?

The extreme f(x)=2x^4+16x^3+27 is Minimum(-6,-837),Saddle(0,27)

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extreme f(x)=2x^4+16x^3+27

extreme points

f (x) = 2 x^{4} + 16 x^{3} + 27

Minimum (- 6, - 837), Saddle (0, 27)

Solution steps

f^{'} (x) = 8 x^{3} + 48 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

2 x^{4} + 16 x^{3} + 27 : - 837

Minimum (- 6, - 837)

Plug

x = 0

into

2 x^{4} + 16 x^{3} + 27 : 27

Saddle (0, 27)

Minimum (- 6, - 837), Saddle (0, 27)

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

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

f (x) = ln (x) - 2 x^{2}

f (x, y) = \frac{1}{2} x y

f (x, y) = - 2 x^{3} - 5 x^{2} + 4 x y - y^{2} + 4 y - 7

What is the extreme f(x)=2x^4+16x^3+27 ?
The extreme f(x)=2x^4+16x^3+27 is Minimum(-6,-837),Saddle(0,27)