What is the extreme 19x^4-114x^2 ?

The extreme 19x^4-114x^2 is Minimum(-sqrt(3),-171),Maximum(0,0),Minimum(sqrt(3),-171)

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extreme 19x^4-114x^2

extreme points

19 x^{4} - 114 x^{2}

Minimum (- 3, - 171), Maximum (0, 0), Minimum (3, - 171)

Solution steps

f^{'} (x) = 76 x^{3} - 228 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

19 x^{4} - 114 x^{2} : - 171

Minimum (- 3, - 171)

Plug

x = 0

into

19 x^{4} - 114 x^{2} : 0

Maximum (0, 0)

Plug

x = 3

into

19 x^{4} - 114 x^{2} : - 171

Minimum (3, - 171)

Minimum (- 3, - 171), Maximum (0, 0), Minimum (3, - 171)

x + 2 y = 6

3 x + 2 y = 14

f (x) = x^{4} - 7 x^{3} - 11 x^{2}

\frac{2 x}{x - 3}

f (x) = \frac{3}{x - 5}

What is the extreme 19x^4-114x^2 ?
The extreme 19x^4-114x^2 is Minimum(-sqrt(3),-171),Maximum(0,0),Minimum(sqrt(3),-171)