What is the extreme f(x)=(x^2-8)^3+50 ?

The extreme f(x)=(x^2-8)^3+50 is Saddle(-2sqrt(2),50),Minimum(0,-462),Saddle(2sqrt(2),50)

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extreme f(x)=(x^2-8)^3+50

extreme points

f (x) = (x^{2} - 8)^{3} + 50

Saddle (- 22, 50), Minimum (0, - 462), Saddle (22, 50)

Solution steps

f^{'} (x) = 6 x^{5} - 96 x^{3} + 384 x

Find intervals:

Decreasing

: - \infty < x < - 22,

Decreasing

: - 22 < x < 0,

Increasing

: 0 < x < 22,

Increasing

: 22 < x < \infty

Plug

x = - 22

into

(x^{2} - 8)^{3} + 50 : 50

Saddle (- 22, 50)

Plug

x = 0

into

(x^{2} - 8)^{3} + 50 : - 462

Minimum (0, - 462)

Plug

x = 22

into

(x^{2} - 8)^{3} + 50 : 50

Saddle (22, 50)

Saddle (- 22, 50), Minimum (0, - 462), Saddle (22, 50)

f (y) = x^{2} + x - 30

f, f \leq - \frac{3}{5} x + 200

f (x) = \frac{1}{25 - x ^{2}}

f (x) = 4 x^{3} - 3 x^{2} - 72 x - 80

x^{2} - 6 x + 3 y^{3} - y + 8

What is the extreme f(x)=(x^2-8)^3+50 ?
The extreme f(x)=(x^2-8)^3+50 is Saddle(-2sqrt(2),50),Minimum(0,-462),Saddle(2sqrt(2),50)