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Popular >

extreme-x^3(x-3)

Solution

extreme points

- x^{3} (x - 3)

Solution

Saddle (0, 0), Maximum (\frac{9}{4}, \frac{2187}{256})

Solution steps

f^{'} (x) = - 4 x^{3} + 9 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{9}{4},

Decreasing

: \frac{9}{4} < x < \infty

Plug

x = 0

into

- x^{3} (x - 3) : 0

Saddle (0, 0)

Plug

x = \frac{9}{4}

into

- x^{3} (x - 3) : \frac{2187}{256}

Maximum (\frac{9}{4}, \frac{2187}{256})

Saddle (0, 0), Maximum (\frac{9}{4}, \frac{2187}{256})

Popular Examples

extreme f(x)= 4/3 x^3-13/2 x^2-3x+11 extreme points

f (x) = \frac{4}{3} x^{3} - \frac{13}{2} x^{2} - 3 x + 11

extreme f(x)=3x^3-14x+20x-8 extreme points

f (x) = 3 x^{3} - 14 x + 20 x - 8

extreme f(x)=(2x^2-5x)^3 extreme points

f (x) = (2 x^{2} - 5 x)^{3}

extreme f(x)=x^{4/5}(x-2)extreme points

f (x) = x^{\frac{4}{5}} (x - 2)

extreme y=xe^{((5-x))/4}extreme points

y = x e^{\frac{( 5 - x )}{4}}

Frequently Asked Questions (FAQ)

What is the extreme-x^3(x-3) ?
The extreme-x^3(x-3) is Saddle(0,0),Maximum(9/4 , 2187/256)