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

The extreme f(x)=x^4+4x^3+10 is Minimum(-3,-17),Saddle(0,10)

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extreme f(x)=x^4+4x^3+10

extreme points

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

Minimum (- 3, - 17), Saddle (0, 10)

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} + 10 : - 17

Minimum (- 3, - 17)

Plug

x = 0

into

x^{4} + 4 x^{3} + 10 : 10

Saddle (0, 10)

Minimum (- 3, - 17), Saddle (0, 10)

P (a, b) = 3 + 2 a^{2} b + 4 a b^{2} + 8 b^{3}

f (x) = 2 x^{3} - 30 x^{2} + 144 x - 11

f (x) = \frac{- 5 x - 4}{6 x ^{2} + 3}

f (x) = 24 sin (3 x)

y = 0.25 x^{4} - (\frac{1}{3}) x^{3}

What is the extreme f(x)=x^4+4x^3+10 ?
The extreme f(x)=x^4+4x^3+10 is Minimum(-3,-17),Saddle(0,10)