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Popular >

extreme x^3+2x^2+x+2

Solution

extreme points

x^{3} + 2 x^{2} + x + 2

Solution

Maximum (- 1, 2), Minimum (- \frac{1}{3}, \frac{50}{27})

Solution steps

f^{'} (x) = 3 x^{2} + 4 x + 1

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < - \frac{1}{3},

Increasing

: - \frac{1}{3} < x < \infty

Plug

x = - 1

into

x^{3} + 2 x^{2} + x + 2 : 2

Maximum (- 1, 2)

Plug

x = - \frac{1}{3}

into

x^{3} + 2 x^{2} + x + 2 : \frac{50}{27}

Minimum (- \frac{1}{3}, \frac{50}{27})

Maximum (- 1, 2), Minimum (- \frac{1}{3}, \frac{50}{27})

Popular Examples

extreme f(x)=x^3-18x^2+81x extreme points

f (x) = x^{3} - 18 x^{2} + 81 x

extreme y=(x^2)/(sqrt(x^2-1))extreme points

y = \frac{x ^{2}}{x ^{2} - 1}

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

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

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

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

extreme f(x)=9-2x+4y-x^2-4y^2 extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme x^3+2x^2+x+2 ?
The extreme x^3+2x^2+x+2 is Maximum(-1,2),Minimum(-1/3 , 50/27)