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Popular >

extreme y=x^4-4x^3+9

Solution

extreme points

y = x^{4} - 4 x^{3} + 9

Solution

Saddle (0, 9), Minimum (3, - 18)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

x^{4} - 4 x^{3} + 9 : 9

Saddle (0, 9)

Plug

x = 3

into

x^{4} - 4 x^{3} + 9 : - 18

Minimum (3, - 18)

Saddle (0, 9), Minimum (3, - 18)

Popular Examples

extreme-sqrt(-x)extreme points

- - x

solvefor y,P=5x^3+3x^2y+xy^2 solve for

y, P = 5 x^{3} + 3 x^{2} y + x y^{2}

extreme f(x,y)=x^3-15x^2+33x+100 extreme points

f (x, y) = x^{3} - 15 x^{2} + 33 x + 100

extreme f(x)=e^{xy-y^2}extreme points

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

extreme f(x)=12x^3+2x^2-3 extreme points

f (x) = 12 x^{3} + 2 x^{2} - 3

Frequently Asked Questions (FAQ)

What is the extreme y=x^4-4x^3+9 ?
The extreme y=x^4-4x^3+9 is Saddle(0,9),Minimum(3,-18)