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

The extreme f(x)=x^4+4x^3-5 is Minimum(-3,-32),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, - 32), 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 : - 32

Minimum (- 3, - 32)

Plug

x = 0

into

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

Saddle (0, - 5)

Minimum (- 3, - 32), Saddle (0, - 5)

f (x) = 6 e^{x - 4}

f (x) = x e^{- x}

\frac{1}{1 + x}

y = - 2 x^{2} + 5

f (x) = 9 - 8 x

What is the extreme f(x)=x^4+4x^3-5 ?
The extreme f(x)=x^4+4x^3-5 is Minimum(-3,-32),Saddle(0,-5)