What is the extreme f(x)=(x^2-4)^7 ?

The extreme f(x)=(x^2-4)^7 is Saddle(-2,0),Minimum(0,-16384),Saddle(2,0)

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extreme f(x)=(x^2-4)^7

extreme points

f (x) = (x^{2} - 4)^{7}

Saddle (- 2, 0), Minimum (0, - 16384), Saddle (2, 0)

Solution steps

f^{'} (x) = 14 x (x^{2} - 4)^{6}

Find intervals:

Decreasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

(x^{2} - 4)^{7} : 0

Saddle (- 2, 0)

Plug

x = 0

into

(x^{2} - 4)^{7} : - 16384

Minimum (0, - 16384)

Plug

x = 2

into

(x^{2} - 4)^{7} : 0

Saddle (2, 0)

Saddle (- 2, 0), Minimum (0, - 16384), Saddle (2, 0)

y = x^{3} - 27 x + 3, - 2 \leq x \leq 4

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

2 x^{3} + 3 x^{2} - 12 x + 5, 0 \leq x \leq 2

f (x, y) = x^{2} + x y + y^{2} - 28 y + 261

(x - 2) (x - 3)^{2}

What is the extreme f(x)=(x^2-4)^7 ?
The extreme f(x)=(x^2-4)^7 is Saddle(-2,0),Minimum(0,-16384),Saddle(2,0)