What is the extreme f(x)=x^4-50x^2+1 ?

The extreme f(x)=x^4-50x^2+1 is Minimum(-5,-624),Maximum(0,1),Minimum(5,-624)

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extreme f(x)=x^4-50x^2+1

extreme points

f (x) = x^{4} - 50 x^{2} + 1

Minimum (- 5, - 624), Maximum (0, 1), Minimum (5, - 624)

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} + 1 : - 624

Minimum (- 5, - 624)

Plug

x = 0

into

x^{4} - 50 x^{2} + 1 : 1

Maximum (0, 1)

Plug

x = 5

into

x^{4} - 50 x^{2} + 1 : - 624

Minimum (5, - 624)

Minimum (- 5, - 624), Maximum (0, 1), Minimum (5, - 624)

f (x) = x^{4} - 50 x^{2} + 2

y = x^{3} - 3 x^{2} + 5

+ \frac{x}{x ^{2} - 25}

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

x^{3} + 3 x y^{2} - 15 x - 12 y + 1

What is the extreme f(x)=x^4-50x^2+1 ?
The extreme f(x)=x^4-50x^2+1 is Minimum(-5,-624),Maximum(0,1),Minimum(5,-624)