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Popular >

extreme 3x^5-5x^3

Solution

extreme points

3 x^{5} - 5 x^{3}

Solution

Maximum (- 1, 2), Saddle (0, 0), Minimum (1, - 2)

Solution steps

f^{'} (x) = 15 x^{4} - 15 x^{2}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

3 x^{5} - 5 x^{3} : 2

Maximum (- 1, 2)

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 1

into

3 x^{5} - 5 x^{3} : - 2

Minimum (1, - 2)

Maximum (- 1, 2), Saddle (0, 0), Minimum (1, - 2)

Popular Examples

extreme 2/(x^{12)}-1/(x^6)extreme points

\frac{2}{x ^{12}} - \frac{1}{x ^{6}}

extreme f(x)=(x^2-4)/(x-1)extreme points

f (x) = \frac{x ^{2} - 4}{x - 1}

extreme f(x,y)=2x-5y+3 extreme points

f (x, y) = 2 x - 5 y + 3

extreme f(x,y)=2x^2-5xy+3y^4+5 extreme points

f (x, y) = 2 x^{2} - 5 x y + 3 y^{4} + 5

extreme f(x,y)=2xy extreme points

f (x, y) = 2 x y

Frequently Asked Questions (FAQ)

What is the extreme 3x^5-5x^3 ?
The extreme 3x^5-5x^3 is Maximum(-1,2),Saddle(0,0),Minimum(1,-2)