What is the extreme x^4-50x^2+2 ?

The extreme x^4-50x^2+2 is Minimum(-5,-623),Maximum(0,2),Minimum(5,-623)

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extreme x^4-50x^2+2

extreme points

x^{4} - 50 x^{2} + 2

Minimum (- 5, - 623), Maximum (0, 2), Minimum (5, - 623)

Solution steps

f^{'} (x) = 4 x^{3} - 100 x

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

x^{4} - 50 x^{2} + 2 : - 623

Minimum (- 5, - 623)

Plug

x = 0

into

x^{4} - 50 x^{2} + 2 : 2

Maximum (0, 2)

Plug

x = 5

into

x^{4} - 50 x^{2} + 2 : - 623

Minimum (5, - 623)

Minimum (- 5, - 623), Maximum (0, 2), Minimum (5, - 623)

1 + (ln (x))

f (x, y) = 3 x^{2} + 3 x - 2 y + 4 y^{2} - 12 x y

f (x, y) = x^{2} - y^{2} - 9 x - 2 y

f (x) = 2 x^{3} - 9 x^{2} + 3, - 2 \leq x \leq 2

f (x, y) = x^{3} + y^{3} + 3 x y^{2} - 18 x - 18 y

What is the extreme x^4-50x^2+2 ?
The extreme x^4-50x^2+2 is Minimum(-5,-623),Maximum(0,2),Minimum(5,-623)