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

The extreme f(x)=x^4-50x^2 is Minimum(-5,-625),Maximum(0,0),Minimum(5,-625)

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

extreme points

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

Minimum (- 5, - 625), Maximum (0, 0), Minimum (5, - 625)

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} : - 625

Minimum (- 5, - 625)

Plug

x = 0

into

x^{4} - 50 x^{2} : 0

Maximum (0, 0)

Plug

x = 5

into

x^{4} - 50 x^{2} : - 625

Minimum (5, - 625)

Minimum (- 5, - 625), Maximum (0, 0), Minimum (5, - 625)

\frac{6 x ^{2} + 1}{2 x ^{2} + x - 1}

f (x) = 5 t^{\frac{2}{3}} + t^{\frac{5}{3}}

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

7 x - 4 = 0

f (x) = (x - 6)^{2}, x \geq 6

What is the extreme f(x)=x^4-50x^2 ?
The extreme f(x)=x^4-50x^2 is Minimum(-5,-625),Maximum(0,0),Minimum(5,-625)