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Popular >

extreme-x^3-x^2

Solution

extreme points

- x^{3} - x^{2}

Solution

Minimum (- \frac{2}{3}, - \frac{4}{27}), Maximum (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{2}{3},

Increasing

: - \frac{2}{3} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{2}{3}

into

- x^{3} - x^{2} : - \frac{4}{27}

Minimum (- \frac{2}{3}, - \frac{4}{27})

Plug

x = 0

into

- x^{3} - x^{2} : 0

Maximum (0, 0)

Minimum (- \frac{2}{3}, - \frac{4}{27}), Maximum (0, 0)

Graph

Popular Examples

extreme h(x)=2x^3-24x extreme points

h (x) = 2 x^{3} - 24 x

extreme y=xsqrt(x^2+1)extreme points

y = x x^{2} + 1

extreme f(x)=4x^2+y^2 extreme points

f (x) = 4 x^{2} + y^{2}

extreme f(x)=ln(4x)extreme points

f (x) = ln (4 x)

extreme x^3-y^3-2xy+6 extreme points

x^{3} - y^{3} - 2 x y + 6

Frequently Asked Questions (FAQ)

What is the extreme-x^3-x^2 ?
The extreme-x^3-x^2 is Minimum(-2/3 ,-4/27),Maximum(0,0)