What is the extreme f(x)=x^6+6x^5 ?

The extreme f(x)=x^6+6x^5 is Minimum(-5,-3125),Saddle(0,0)

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extreme f(x)=x^6+6x^5

extreme points

f (x) = x^{6} + 6 x^{5}

Minimum (- 5, - 3125), Saddle (0, 0)

Solution steps

f^{'} (x) = 6 x^{5} + 30 x^{4}

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 5

into

x^{6} + 6 x^{5} : - 3125

Minimum (- 5, - 3125)

Plug

x = 0

into

x^{6} + 6 x^{5} : 0

Saddle (0, 0)

Minimum (- 5, - 3125), Saddle (0, 0)

u (x, y) = k x + y x

9 x^{2} - 4

x 4 - x^{2}, - 1 \leq x \leq 2

\frac{d}{d M} (- M + \frac{1}{8} r a)

f (x) = \frac{( x + 4 )}{x ^{2}}

What is the extreme f(x)=x^6+6x^5 ?
The extreme f(x)=x^6+6x^5 is Minimum(-5,-3125),Saddle(0,0)