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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 1)

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 1

into

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

Maximum (1, 1)

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

Graph

Popular Examples

extreme f(x)=12x^5+30x^4-300x^3+3 extreme points

f (x) = 12 x^{5} + 30 x^{4} - 300 x^{3} + 3

extreme f(x)=(6x^2)/(x^2-9)extreme points

f (x) = \frac{6 x ^{2}}{x ^{2} - 9}

extreme f(x)=x+(49)/x+5,1<= x<= 98 extreme points

f (x) = x + \frac{49}{x} + 5, 1 \leq x \leq 98

extreme f(x)=((x+2))/(x^2-x-6)extreme points

f (x) = \frac{( x + 2 )}{x ^{2} - x - 6}

extreme g(y)=4-y^2,-2<= y<= 1 extreme points

g (y) = 4 - y^{2}, - 2 \leq y \leq 1

Frequently Asked Questions (FAQ)

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