What is the extreme f(x)=x^4+4x^3+5 ?

The extreme f(x)=x^4+4x^3+5 is Minimum(-3,-22),Saddle(0,5)

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extreme f(x)=x^4+4x^3+5

extreme points

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

Minimum (- 3, - 22), Saddle (0, 5)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

x^{4} + 4 x^{3} + 5 : - 22

Minimum (- 3, - 22)

Plug

x = 0

into

x^{4} + 4 x^{3} + 5 : 5

Saddle (0, 5)

Minimum (- 3, - 22), Saddle (0, 5)

f (x, y) = 5 x + 2 y

f (x) = 5 x^{7} - 7 x^{5} - 7

\frac{x ^{2} + 4}{x ^{2} - 25}

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

f (x) = \frac{x}{x ^{2} + 1}

What is the extreme f(x)=x^4+4x^3+5 ?
The extreme f(x)=x^4+4x^3+5 is Minimum(-3,-22),Saddle(0,5)