What is the extreme f(x)=190+8x^3+x^4 ?

The extreme f(x)=190+8x^3+x^4 is Minimum(-6,-242),Saddle(0,190)

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extreme f(x)=190+8x^3+x^4

extreme points

f (x) = 190 + 8 x^{3} + x^{4}

Minimum (- 6, - 242), Saddle (0, 190)

Solution steps

f^{'} (x) = 4 x^{3} + 24 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

190 + 8 x^{3} + x^{4} : - 242

Minimum (- 6, - 242)

Plug

x = 0

into

190 + 8 x^{3} + x^{4} : 190

Saddle (0, 190)

Minimum (- 6, - 242), Saddle (0, 190)

y = 4 - 6 x + x^{2}

f (x) = 0.002 x^{2} + 3.4 x - 20

f (x, y) = x^{3} + 2 y^{2} - 27 x - 8 y - 4

f (x) = x^{\frac{1}{3}} + 9

f (x) = (x^{2} + y^{2})^{2} = 2 \cdot (x^{2} - y^{2})

What is the extreme f(x)=190+8x^3+x^4 ?
The extreme f(x)=190+8x^3+x^4 is Minimum(-6,-242),Saddle(0,190)