What is the extreme f(x)=f(x)=30+20x^3-5x^4-x^5 ?

The extreme f(x)=f(x)=30+20x^3-5x^4-x^5 is Minimum(-6,-2994),Saddle(0,30),Maximum(2,78)

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extreme f(x)=f(x)=30+20x^3-5x^4-x^5

extreme points

f (x) = f (x) = 30 + 20 x^{3} - 5 x^{4} - x^{5}

Minimum (- 6, - 2994), Saddle (0, 30), Maximum (2, 78)

Solution steps

f^{'} (x) = - 5 x^{4} - 20 x^{3} + 60 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 6

into

30 + 20 x^{3} - 5 x^{4} - x^{5} : - 2994

Minimum (- 6, - 2994)

Plug

x = 0

into

30 + 20 x^{3} - 5 x^{4} - x^{5} : 30

Saddle (0, 30)

Plug

x = 2

into

30 + 20 x^{3} - 5 x^{4} - x^{5} : 78

Maximum (2, 78)

Minimum (- 6, - 2994), Saddle (0, 30), Maximum (2, 78)

f (x, y) = - 4 x + 15 y

f (x) = sin (2 x) - cos (x) - 4 x

y = 1 + x^{2}

f (x) = 2 x^{4} - 196 x^{2} - 2

f (x) = 2 x^{4} - 196 x^{2} + 4

What is the extreme f(x)=f(x)=30+20x^3-5x^4-x^5 ?
The extreme f(x)=f(x)=30+20x^3-5x^4-x^5 is Minimum(-6,-2994),Saddle(0,30),Maximum(2,78)