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

The extreme f(x)=(x-2)^7(x+4)^7 is Saddle(-4,0),Minimum(-1,-4782969),Saddle(2,0)

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

extreme points

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

Saddle (- 4, 0), Minimum (- 1, - 4782969), Saddle (2, 0)

Solution steps

f^{'} (x) = 14 (x - 2)^{6} (x + 4)^{6} (x + 1)

Find intervals:

Decreasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < - 1,

Increasing

: - 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 4

into

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

Saddle (- 4, 0)

Plug

x = - 1

into

(x - 2)^{7} (x + 4)^{7} : - 4782969

Minimum (- 1, - 4782969)

Plug

x = 2

into

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

Saddle (2, 0)

Saddle (- 4, 0), Minimum (- 1, - 4782969), Saddle (2, 0)

sin^{8} (x) + cos^{8} (x)

f (x, y) = 400 - 81 x^{2} - 4 y^{2}

f (x) = 9 t^{2} + 4 t - 10

(x^{2} - 4)^{\frac{1}{7}}, - 2 \leq x \leq 3

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

What is the extreme f(x)=(x-2)^7(x+4)^7 ?
The extreme f(x)=(x-2)^7(x+4)^7 is Saddle(-4,0),Minimum(-1,-4782969),Saddle(2,0)