What is the extreme y=17x^4-102x^2 ?

The extreme y=17x^4-102x^2 is Minimum(-sqrt(3),-153),Maximum(0,0),Minimum(sqrt(3),-153)

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extreme y=17x^4-102x^2

extreme points

y = 17 x^{4} - 102 x^{2}

Minimum (- 3, - 153), Maximum (0, 0), Minimum (3, - 153)

Solution steps

f^{'} (x) = 68 x^{3} - 204 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

17 x^{4} - 102 x^{2} : - 153

Minimum (- 3, - 153)

Plug

x = 0

into

17 x^{4} - 102 x^{2} : 0

Maximum (0, 0)

Plug

x = 3

into

17 x^{4} - 102 x^{2} : - 153

Minimum (3, - 153)

Minimum (- 3, - 153), Maximum (0, 0), Minimum (3, - 153)

x^{2} + y - e^{y}

f (x) = [24144]

f (x) = x^{4} - 2 x^{2} + 8, - 4 \leq x \leq 4

16 x^{4} + 125 x

f (x) = x^{2} + y^{2} - 2 x - 6 y + 14

What is the extreme y=17x^4-102x^2 ?
The extreme y=17x^4-102x^2 is Minimum(-sqrt(3),-153),Maximum(0,0),Minimum(sqrt(3),-153)