What is the extreme f(x)=x^5-10x^4-3x^2 ?

The extreme f(x)=x^5-10x^4-3x^2 is Maximum(0,0),Minimum(8.01866…,-8384.44895…)

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extreme f(x)=x^5-10x^4-3x^2

extreme points

f (x) = x^{5} - 10 x^{4} - 3 x^{2}

Maximum (0, 0), Minimum (8.01866 \dots, - 8384.44895 \dots)

Solution steps

Find the critical points:

x = 0, x = 8.01866 \dots

Domain of

x^{5} - 10 x^{4} - 3 x^{2} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 8.01866 \dots,

Increasing

: 8.01866 \dots < x < \infty

Plug the extreme point

x = 0

into

x^{5} - 10 x^{4} - 3 x^{2} \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 8.01866 \dots

into

x^{5} - 10 x^{4} - 3 x^{2} \Rightarrow y = - 8384.44895 \dots

Minimum (8.01866 \dots, - 8384.44895 \dots)

Maximum (0, 0), Minimum (8.01866 \dots, - 8384.44895 \dots)

f (x) = x e^{- x}

2 y^{3} + 6 y x^{2} - 3 x^{3} - 150 y

f (x) = - \frac{1}{2} x^{2} + 2 x + 3

f (x) = 2 x - 4 x - 3

f (x) = 2 x^{3} e^{- x}

What is the extreme f(x)=x^5-10x^4-3x^2 ?
The extreme f(x)=x^5-10x^4-3x^2 is Maximum(0,0),Minimum(8.01866…,-8384.44895…)