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Popular >

extreme-x^3+x^2+8x+8

Solution

extreme points

- x^{3} + x^{2} + 8 x + 8

Solution

Minimum (- \frac{4}{3}, \frac{40}{27}), Maximum (2, 20)

Solution steps

f^{'} (x) = - 3 x^{2} + 2 x + 8

Find intervals:

Decreasing

: - \infty < x < - \frac{4}{3},

Increasing

: - \frac{4}{3} < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - \frac{4}{3}

into

- x^{3} + x^{2} + 8 x + 8 : \frac{40}{27}

Minimum (- \frac{4}{3}, \frac{40}{27})

Plug

x = 2

into

- x^{3} + x^{2} + 8 x + 8 : 20

Maximum (2, 20)

Minimum (- \frac{4}{3}, \frac{40}{27}), Maximum (2, 20)

Popular Examples

extreme f(x)=-3x^3+27x extreme points

f (x) = - 3 x^{3} + 27 x

extreme F(X,Y)=3X+2X^2+4Y+Y^2-2XY extreme points

F (X, Y) = 3 X + 2 X^{2} + 4 Y + Y^{2} - 2 X Y

extreme f(x)=8x^2-6x^4 extreme points

f (x) = 8 x^{2} - 6 x^{4}

extreme T(x,y)=27-8x^2-9y^2 extreme points

T (x, y) = 27 - 8 x^{2} - 9 y^{2}

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

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

Frequently Asked Questions (FAQ)

What is the extreme-x^3+x^2+8x+8 ?
The extreme-x^3+x^2+8x+8 is Minimum(-4/3 , 40/27),Maximum(2,20)