What is the extreme (x^5)/(20)-3x^3 ?

The extreme (x^5)/(20)-3x^3 is Maximum(-6, 1296/5),Saddle(0,0),Minimum(6,-1296/5)

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extreme (x^5)/(20)-3x^3

extreme points

\frac{x ^{5}}{20} - 3 x^{3}

Maximum (- 6, \frac{1296}{5}), Saddle (0, 0), Minimum (6, - \frac{1296}{5})

Solution steps

f^{'} (x) = \frac{x ^{4}}{4} - 9 x^{2}

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 6

into

\frac{x ^{5}}{20} - 3 x^{3} : \frac{1296}{5}

Maximum (- 6, \frac{1296}{5})

Plug

x = 0

into

\frac{x ^{5}}{20} - 3 x^{3} : 0

Saddle (0, 0)

Plug

x = 6

into

\frac{x ^{5}}{20} - 3 x^{3} : - \frac{1296}{5}

Minimum (6, - \frac{1296}{5})

Maximum (- 6, \frac{1296}{5}), Saddle (0, 0), Minimum (6, - \frac{1296}{5})

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

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

f (x) = \frac{x ^{2} \cdot y}{x}

f (x) = 2 x^{3} + 3 x^{2} - 120 x + 4, - 5 \leq x \leq 5

y = 4 (1.5)^{x}

What is the extreme (x^5)/(20)-3x^3 ?
The extreme (x^5)/(20)-3x^3 is Maximum(-6, 1296/5),Saddle(0,0),Minimum(6,-1296/5)