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Popular >

extreme 2x^2-x^4

Solution

extreme points

2 x^{2} - x^{4}

Solution

Maximum (- 1, 1), Minimum (0, 0), Maximum (1, 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

2 x^{2} - x^{4} : 1

Maximum (- 1, 1)

Plug

x = 0

into

2 x^{2} - x^{4} : 0

Minimum (0, 0)

Plug

x = 1

into

2 x^{2} - x^{4} : 1

Maximum (1, 1)

Maximum (- 1, 1), Minimum (0, 0), Maximum (1, 1)

Popular Examples

extreme f(x,y)=-3x^2+6x+12xy-3y^2+2y^3+6 extreme points

f (x, y) = - 3 x^{2} + 6 x + 12 x y - 3 y^{2} + 2 y^{3} + 6

extreme f(x)=Y(x)=x^3-3x^2-9x+20 extreme points

f (x) = Y (x) = x^{3} - 3 x^{2} - 9 x + 20

extreme f(x)=-3x^{2/3},-1<= x<= 1 extreme points

f (x) = - 3 x^{\frac{2}{3}}, - 1 \leq x \leq 1

extreme f(x)=x^3+3x^2-24x,-1<= x<= 3 extreme points

f (x) = x^{3} + 3 x^{2} - 24 x, - 1 \leq x \leq 3

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

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

Frequently Asked Questions (FAQ)

What is the extreme 2x^2-x^4 ?
The extreme 2x^2-x^4 is Maximum(-1,1),Minimum(0,0),Maximum(1,1)