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Popular >

extreme x^4-6x^3

Solution

extreme points

x^{4} - 6 x^{3}

Solution

Saddle (0, 0), Minimum (\frac{9}{2}, - \frac{2187}{16})

Solution steps

f^{'} (x) = 4 x^{3} - 18 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{9}{2},

Increasing

: \frac{9}{2} < x < \infty

Plug

x = 0

into

x^{4} - 6 x^{3} : 0

Saddle (0, 0)

Plug

x = \frac{9}{2}

into

x^{4} - 6 x^{3} : - \frac{2187}{16}

Minimum (\frac{9}{2}, - \frac{2187}{16})

Saddle (0, 0), Minimum (\frac{9}{2}, - \frac{2187}{16})

Popular Examples

extreme f(x)=x^{2/3}(x^2-4)extreme points

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

extreme P(x,y)=4x^2-100y^2 extreme points

P (x, y) = 4 x^{2} - 100 y^{2}

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

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

extreme f(x,y)=x^2\times y^3-10y+15xy^2 extreme points

f (x, y) = x^{2} \times y^{3} - 10 y + 15 x y^{2}

extreme f(x)= 1/(x+2),-4<= x<= 1 extreme points

f (x) = \frac{1}{x + 2}, - 4 \leq x \leq 1

Frequently Asked Questions (FAQ)

What is the extreme x^4-6x^3 ?
The extreme x^4-6x^3 is Saddle(0,0),Minimum(9/2 ,-2187/16)