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Popular >

extreme f(x)=(x-5)(x-3)(x+1)^2

Solution

extreme points

f (x) = (x - 5) (x - 3) (x + 1)^{2}

Solution

Minimum (- 1, 0), Maximum (\frac{11 - 33}{4}, \frac{165 33 - 363}{32} + 15), Minimum (\frac{11 + 33}{4}, \frac{- 363 - 165 33}{32} + 15)

Solution steps

f^{'} (x) = 2 (x + 1) (2 x^{2} - 11 x + 11)

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < \frac{11 - 33}{4},

Decreasing

: \frac{11 - 33}{4} < x < \frac{11 + 33}{4},

Increasing

: \frac{11 + 33}{4} < x < \infty

Plug

x = - 1

into

(x - 5) (x - 3) (x + 1)^{2} : 0

Minimum (- 1, 0)

Plug

x = \frac{11 - 33}{4}

into

(x - 5) (x - 3) (x + 1)^{2} : \frac{165 33 - 363}{32} + 15

Maximum (\frac{11 - 33}{4}, \frac{165 33 - 363}{32} + 15)

Plug

x = \frac{11 + 33}{4}

into

(x - 5) (x - 3) (x + 1)^{2} : \frac{- 363 - 165 33}{32} + 15

Minimum (\frac{11 + 33}{4}, \frac{- 363 - 165 33}{32} + 15)

Minimum (- 1, 0), Maximum (\frac{11 - 33}{4}, \frac{165 33 - 363}{32} + 15), Minimum (\frac{11 + 33}{4}, \frac{- 363 - 165 33}{32} + 15)

Graph

Popular Examples

extreme y=x^3-3x^2-9x+1 extreme points

y = x^{3} - 3 x^{2} - 9 x + 1

extreme f(x)= 2/3 x^3+14x^2+96x+7 extreme points

f (x) = \frac{2}{3} x^{3} + 14 x^{2} + 96 x + 7

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

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

extreme 3x^2+y^2-xy-11x extreme points

3 x^{2} + y^{2} - x y - 11 x

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x-5)(x-3)(x+1)^2 ?
The extreme f(x)=(x-5)(x-3)(x+1)^2 is