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Popular >

extreme f(x)=(x+1)^2(2x-x^2)

Solution

extreme points

f (x) = (x + 1)^{2} (2 x - x^{2})

Solution

Maximum (- 1, 0), Minimum (\frac{1 - 3}{2}, \frac{6 3 - 11}{4} + 5 - 33), Maximum (\frac{1 + 3}{2}, \frac{- 11 - 6 3}{4} + 33 + 5)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{1 - 3}{2},

Increasing

: \frac{1 - 3}{2} < x < \frac{1 + 3}{2},

Decreasing

: \frac{1 + 3}{2} < x < \infty

Plug

x = - 1

into

(x + 1)^{2} (2 x - x^{2}) : 0

Maximum (- 1, 0)

Plug

x = \frac{1 - 3}{2}

into

(x + 1)^{2} (2 x - x^{2}) : \frac{6 3 - 11}{4} + 5 - 33

Minimum (\frac{1 - 3}{2}, \frac{6 3 - 11}{4} + 5 - 33)

Plug

x = \frac{1 + 3}{2}

into

(x + 1)^{2} (2 x - x^{2}) : \frac{- 11 - 6 3}{4} + 33 + 5

Maximum (\frac{1 + 3}{2}, \frac{- 11 - 6 3}{4} + 33 + 5)

Maximum (- 1, 0), Minimum (\frac{1 - 3}{2}, \frac{6 3 - 11}{4} + 5 - 33), Maximum (\frac{1 + 3}{2}, \frac{- 11 - 6 3}{4} + 33 + 5)

Popular Examples

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

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

extreme f(x)=-x^3-10x extreme points

f (x) = - x^{3} - 10 x

extreme f(x,y)=6x^2-5y^2+6x+y+5 extreme points

f (x, y) = 6 x^{2} - 5 y^{2} + 6 x + y + 5

extreme f(x)=ln((x+3)/(x-3))extreme points

f (x) = ln (\frac{x + 3}{x - 3})

extreme f(x)=-(15x^4)/4-(5x^3)/3-4 extreme points

f (x) = - \frac{15 x ^{4}}{4} - \frac{5 x ^{3}}{3} - 4

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x+1)^2(2x-x^2) ?
The extreme f(x)=(x+1)^2(2x-x^2) is