What is the extreme f(x)=-2/5 x^5-5x^4-16x^3-5 ?

The extreme f(x)=-2/5 x^5-5x^4-16x^3-5 is Minimum(-6, 407/5),Maximum(-4, 743/5),Saddle(0,-5)

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extreme f(x)=-2/5 x^5-5x^4-16x^3-5

extreme points

f (x) = - \frac{2}{5} x^{5} - 5 x^{4} - 16 x^{3} - 5

Minimum (- 6, \frac{407}{5}), Maximum (- 4, \frac{743}{5}), Saddle (0, - 5)

Solution steps

f^{'} (x) = - 2 x^{4} - 20 x^{3} - 48 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < - 4,

Decreasing

: - 4 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 6

into

- \frac{2}{5} x^{5} - 5 x^{4} - 16 x^{3} - 5 : \frac{407}{5}

Minimum (- 6, \frac{407}{5})

Plug

x = - 4

into

- \frac{2}{5} x^{5} - 5 x^{4} - 16 x^{3} - 5 : \frac{743}{5}

Maximum (- 4, \frac{743}{5})

Plug

x = 0

into

- \frac{2}{5} x^{5} - 5 x^{4} - 16 x^{3} - 5 : - 5

Saddle (0, - 5)

Minimum (- 6, \frac{407}{5}), Maximum (- 4, \frac{743}{5}), Saddle (0, - 5)

g (x, y) = 16 - x^{2} + y^{2}

f (x) = e^{- x - y}

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

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

f (x, y) = 2 x^{2} + 4 x y + 6 y^{2} - 8 x - 10

What is the extreme f(x)=-2/5 x^5-5x^4-16x^3-5 ?
The extreme f(x)=-2/5 x^5-5x^4-16x^3-5 is Minimum(-6, 407/5),Maximum(-4, 743/5),Saddle(0,-5)