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Popular >

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

Solution

extreme points

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

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

Plug

x = 3

into

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

Minimum (3, 0)

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

Popular Examples

extreme f(x)=6x^2-6x+9 extreme points

f (x) = 6 x^{2} - 6 x + 9

extreme f(x)=2y^2+2xy+x^2-16x-20y extreme points

f (x) = 2 y^{2} + 2 x y + x^{2} - 16 x - 20 y

extreme-2/(4x+x^2-2)extreme points

- \frac{2}{4 x + x ^{2} - 2}

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

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

extreme f(x,y)=x^2*y^2+x^2-x*y^2-5*x-7 extreme points

f (x, y) = x^{2} \cdot y^{2} + x^{2} - x \cdot y^{2} - 5 \cdot x - 7

Frequently Asked Questions (FAQ)

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