What is the extreme f(x)=(3x^5-20x^3)/(32) ?

The extreme f(x)=(3x^5-20x^3)/(32) is Maximum(-2,2),Saddle(0,0),Minimum(2,-2)

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extreme f(x)=(3x^5-20x^3)/(32)

extreme points

f (x) = \frac{3 x ^{5} - 20 x ^{3}}{32}

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

Solution steps

f^{'} (x) = \frac{1}{32} (15 x^{4} - 60 x^{2})

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

\frac{3 x ^{5} - 20 x ^{3}}{32} : 2

Maximum (- 2, 2)

Plug

x = 0

into

\frac{3 x ^{5} - 20 x ^{3}}{32} : 0

Saddle (0, 0)

Plug

x = 2

into

\frac{3 x ^{5} - 20 x ^{3}}{32} : - 2

Minimum (2, - 2)

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

f (x) = x + 2

f (x) = x^{2} - 10, - 3 \leq x \leq 4

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

f (x) = 12 x y - x^{3} - 6 y^{2}

4 x^{2} + 8 x y + 2 y

What is the extreme f(x)=(3x^5-20x^3)/(32) ?
The extreme f(x)=(3x^5-20x^3)/(32) is Maximum(-2,2),Saddle(0,0),Minimum(2,-2)