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Popular >

extreme x^4-2x^3+2

Solution

extreme points

x^{4} - 2 x^{3} + 2

Solution

Saddle (0, 2), Minimum (\frac{3}{2}, \frac{5}{16})

Solution steps

f^{'} (x) = 4 x^{3} - 6 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{3}{2},

Increasing

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

Plug

x = 0

into

x^{4} - 2 x^{3} + 2 : 2

Saddle (0, 2)

Plug

x = \frac{3}{2}

into

x^{4} - 2 x^{3} + 2 : \frac{5}{16}

Minimum (\frac{3}{2}, \frac{5}{16})

Saddle (0, 2), Minimum (\frac{3}{2}, \frac{5}{16})

Popular Examples

extreme f(x)=(x^3)/(x^2-9)extreme points

f (x) = \frac{x ^{3}}{x ^{2} - 9}

extreme y=-x^3-3x+4 extreme points

y = - x^{3} - 3 x + 4

simplify 12-b+c simplify

12 - b + c

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15

extreme f(x,y)=12x-x^3-4y^2 extreme points

f (x, y) = 12 x - x^{3} - 4 y^{2}

Frequently Asked Questions (FAQ)

What is the extreme x^4-2x^3+2 ?
The extreme x^4-2x^3+2 is Saddle(0,2),Minimum(3/2 , 5/16)