What is the extreme 7(4x^2-36)^3+8 ?

The extreme 7(4x^2-36)^3+8 is Saddle(-3,8),Minimum(0,-326584),Saddle(3,8)

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extreme 7(4x^2-36)^3+8

extreme points

7 (4 x^{2} - 36)^{3} + 8

Saddle (- 3, 8), Minimum (0, - 326584), Saddle (3, 8)

Solution steps

f^{'} (x) = 2688 x^{5} - 48384 x^{3} + 217728 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Increasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

7 (4 x^{2} - 36)^{3} + 8 : 8

Saddle (- 3, 8)

Plug

x = 0

into

7 (4 x^{2} - 36)^{3} + 8 : - 326584

Minimum (0, - 326584)

Plug

x = 3

into

7 (4 x^{2} - 36)^{3} + 8 : 8

Saddle (3, 8)

Saddle (- 3, 8), Minimum (0, - 326584), Saddle (3, 8)

x^{2} - x + 7

f (x) = \frac{5 x}{x ^{2} + 16}

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

f (x) = 3 x^{2} ln (\frac{x}{2})

f (x, y) = \frac{1}{2} x^{2} + 2 y^{2} - 4 x - 16 y

What is the extreme 7(4x^2-36)^3+8 ?
The extreme 7(4x^2-36)^3+8 is Saddle(-3,8),Minimum(0,-326584),Saddle(3,8)