What is the extreme x^4-3x^2 ?

The extreme x^4-3x^2 is Minimum(-sqrt(3/2),-9/4),Maximum(0,0),Minimum(sqrt(3/2),-9/4)

Popular >

extreme x^4-3x^2

extreme points

x^{4} - 3 x^{2}

Minimum (- \frac{3}{2}, - \frac{9}{4}), Maximum (0, 0), Minimum (\frac{3}{2}, - \frac{9}{4})

Solution steps

f^{'} (x) = 4 x^{3} - 6 x

Find intervals:

Decreasing

: - \infty < x < - \frac{3}{2},

Increasing

: - \frac{3}{2} < x < 0,

Decreasing

: 0 < x < \frac{3}{2},

Increasing

: \frac{3}{2} < x < \infty

Plug

x = - \frac{3}{2}

into

x^{4} - 3 x^{2} : - \frac{9}{4}

Minimum (- \frac{3}{2}, - \frac{9}{4})

Plug

x = 0

into

x^{4} - 3 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{3}{2}

into

x^{4} - 3 x^{2} : - \frac{9}{4}

Minimum (\frac{3}{2}, - \frac{9}{4})

Minimum (- \frac{3}{2}, - \frac{9}{4}), Maximum (0, 0), Minimum (\frac{3}{2}, - \frac{9}{4})

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

2 x + \frac{27}{x ^{2}}

f (x) = 5 x^{2} 1 + x

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

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

What is the extreme x^4-3x^2 ?
The extreme x^4-3x^2 is Minimum(-sqrt(3/2),-9/4),Maximum(0,0),Minimum(sqrt(3/2),-9/4)