What is the extreme f(x)=1+80x^3+5x^4-2x^5 ?

The extreme f(x)=1+80x^3+5x^4-2x^5 is Minimum(-4,-1791),Saddle(0,1),Maximum(6,8209)

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extreme f(x)=1+80x^3+5x^4-2x^5

extreme points

f (x) = 1 + 80 x^{3} + 5 x^{4} - 2 x^{5}

Minimum (- 4, - 1791), Saddle (0, 1), Maximum (6, 8209)

Solution steps

f^{'} (x) = - 10 x^{4} + 20 x^{3} + 240 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Increasing

: 0 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = - 4

into

1 + 80 x^{3} + 5 x^{4} - 2 x^{5} : - 1791

Minimum (- 4, - 1791)

Plug

x = 0

into

1 + 80 x^{3} + 5 x^{4} - 2 x^{5} : 1

Saddle (0, 1)

Plug

x = 6

into

1 + 80 x^{3} + 5 x^{4} - 2 x^{5} : 8209

Maximum (6, 8209)

Minimum (- 4, - 1791), Saddle (0, 1), Maximum (6, 8209)

What is the extreme f(x)=1+80x^3+5x^4-2x^5 ?
The extreme f(x)=1+80x^3+5x^4-2x^5 is Minimum(-4,-1791),Saddle(0,1),Maximum(6,8209)