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Popular >

extreme (x-2)(x-3)^2

Solution

extreme points

(x - 2) (x - 3)^{2}

Solution

Maximum (\frac{7}{3}, \frac{4}{27}), Minimum (3, 0)

Solution steps

f^{'} (x) = (x - 3) (3 x - 7)

Find intervals:

Increasing

: - \infty < x < \frac{7}{3},

Decreasing

: \frac{7}{3} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = \frac{7}{3}

into

(x - 2) (x - 3)^{2} : \frac{4}{27}

Maximum (\frac{7}{3}, \frac{4}{27})

Plug

x = 3

into

(x - 2) (x - 3)^{2} : 0

Minimum (3, 0)

Maximum (\frac{7}{3}, \frac{4}{27}), Minimum (3, 0)

Popular Examples

extreme f(x)=24x-2x^3 extreme points

f (x) = 24 x - 2 x^{3}

extreme f(x,y)=2x^2+3xy+4y^2+5x-2y extreme points

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 5 x - 2 y

extreme f(x,y)=2x^2+3xy+y^2+5 extreme points

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

extreme f(x)=x^4+8x^3+22x^2+24x+9 extreme points

f (x) = x^{4} + 8 x^{3} + 22 x^{2} + 24 x + 9

extreme f(x,y)=2x^3+6xy^2-3y^3-150x extreme points

f (x, y) = 2 x^{3} + 6 x y^{2} - 3 y^{3} - 150 x

Frequently Asked Questions (FAQ)

What is the extreme (x-2)(x-3)^2 ?
The extreme (x-2)(x-3)^2 is Maximum(7/3 , 4/27),Minimum(3,0)