What is the extreme f(x)=19x^4-114x^2 ?

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

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extreme f(x)=19x^4-114x^2

extreme points

f (x) = 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)

f (x) = \frac{3 + 4 x}{3 x}

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

f (x) = \frac{5}{x + 9}

3 x + y = 9

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