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Popular >

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

Solution

extreme points

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

Solution

Minimum (- 1, - 1), Saddle (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 1

into

3 x^{4} + 4 x^{3} : - 1

Minimum (- 1, - 1)

Plug

x = 0

into

3 x^{4} + 4 x^{3} : 0

Saddle (0, 0)

Minimum (- 1, - 1), Saddle (0, 0)

Popular Examples

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

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

extreme f(x)=x^4-4x^3-18x^2 extreme points

f (x) = x^{4} - 4 x^{3} - 18 x^{2}

extreme y=x^4-2x^2 extreme points

y = x^{4} - 2 x^{2}

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

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

extreme f(x,y)=ln(x^2+y^2-1)extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme y=3x^4+4x^3 ?
The extreme y=3x^4+4x^3 is Minimum(-1,-1),Saddle(0,0)