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Popular >

extreme x^3+3x^2+1

Solution

extreme points

x^{3} + 3 x^{2} + 1

Solution

Maximum (- 2, 5), Minimum (0, 1)

Solution steps

f^{'} (x) = 3 x^{2} + 6 x

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

x^{3} + 3 x^{2} + 1 : 5

Maximum (- 2, 5)

Plug

x = 0

into

x^{3} + 3 x^{2} + 1 : 1

Minimum (0, 1)

Maximum (- 2, 5), Minimum (0, 1)

Popular Examples

extreme f(x)=-5x^4+5x^3-10 extreme points

f (x) = - 5 x^{4} + 5 x^{3} - 10

extreme f(x,y)=3x^{-2}+5y^{-2}+8xy^2 extreme points

f (x, y) = 3 x^{- 2} + 5 y^{- 2} + 8 x y^{2}

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

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

extreme f(x)=ln(x+y)extreme points

f (x) = ln (x + y)

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

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

Frequently Asked Questions (FAQ)

What is the extreme x^3+3x^2+1 ?
The extreme x^3+3x^2+1 is Maximum(-2,5),Minimum(0,1)