What is the extreme y=3x^5-20x^3 ?

The extreme y=3x^5-20x^3 is Maximum(-2,64),Saddle(0,0),Minimum(2,-64)

Popular >

extreme y=3x^5-20x^3

extreme points

y = 3 x^{5} - 20 x^{3}

Maximum (- 2, 64), Saddle (0, 0), Minimum (2, - 64)

Solution steps

f^{'} (x) = 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

3 x^{5} - 20 x^{3} : 64

Maximum (- 2, 64)

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 2

into

3 x^{5} - 20 x^{3} : - 64

Minimum (2, - 64)

Maximum (- 2, 64), Saddle (0, 0), Minimum (2, - 64)

F (x, y) = 5 x y^{3} - y^{4} + \frac{x ^{2}}{2}

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

f (x, y) = 2 x^{3} - y^{3} - 24 x + 27 y - 2

f (x) = (x + 2)^{3}

f (x) = \frac{4 x}{x ^{2} - 36}

What is the extreme y=3x^5-20x^3 ?
The extreme y=3x^5-20x^3 is Maximum(-2,64),Saddle(0,0),Minimum(2,-64)