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Popular >

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

Solution

extreme points

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

Solution

Maximum (- 1, 2), Minimum (0, 0), Maximum (1, 2)

Solution steps

f^{'} (x) = 8 x - 8 x^{3}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 2)

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 1

into

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

Maximum (1, 2)

Maximum (- 1, 2), Minimum (0, 0), Maximum (1, 2)

Popular Examples

extreme f(x)=(x^2-1)e^{-ax}extreme points

f (x) = (x^{2} - 1) e^{- a x}

extreme f(x)=x^4+y^4-4x^2y+2y extreme points

f (x) = x^{4} + y^{4} - 4 x^{2} y + 2 y

extreme (x^2-24)/(x-5)extreme points

\frac{x ^{2} - 24}{x - 5}

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

f (x) = 2 x^{3} - 3 x^{2} + 1

extreme f(x,y)=20x+64y+8xy-x^2-32y^2 extreme points

f (x, y) = 20 x + 64 y + 8 x y - x^{2} - 32 y^{2}

Frequently Asked Questions (FAQ)

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