What is the extreme f(x)=4x^5-25x^4-40x^3+2 ?

The extreme f(x)=4x^5-25x^4-40x^3+2 is Maximum(-1,13),Saddle(0,2),Minimum(6,-9934)

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extreme f(x)=4x^5-25x^4-40x^3+2

extreme

Maximum (- 1, 13), Saddle (0, 2), Minimum (6, - 9934)

Solution steps

f^{'} (x) = 20 x^{4} - 100 x^{3} - 120 x^{2}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 1

into

4 x^{5} - 25 x^{4} - 40 x^{3} + 2 : 13

Maximum (- 1, 13)

Plug

x = 0

into

4 x^{5} - 25 x^{4} - 40 x^{3} + 2 : 2

Saddle (0, 2)

Plug

x = 6

into

4 x^{5} - 25 x^{4} - 40 x^{3} + 2 : - 9934

Minimum (6, - 9934)

Maximum (- 1, 13), Saddle (0, 2), Minimum (6, - 9934)

What is the extreme f(x)=4x^5-25x^4-40x^3+2 ?
The extreme f(x)=4x^5-25x^4-40x^3+2 is Maximum(-1,13),Saddle(0,2),Minimum(6,-9934)