What is the extreme f(x)=4x^5+10x^4-100x^3+1 ?

The extreme f(x)=4x^5+10x^4-100x^3+1 is Maximum(-5,6251),Saddle(0,1),Minimum(3,-917)

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extreme f(x)=4x^5+10x^4-100x^3+1

extreme

Maximum (- 5, 6251), Saddle (0, 1), Minimum (3, - 917)

Solution steps

f^{'} (x) = 20 x^{4} + 40 x^{3} - 300 x^{2}

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 5

into

4 x^{5} + 10 x^{4} - 100 x^{3} + 1 : 6251

Maximum (- 5, 6251)

Plug

x = 0

into

4 x^{5} + 10 x^{4} - 100 x^{3} + 1 : 1

Saddle (0, 1)

Plug

x = 3

into

4 x^{5} + 10 x^{4} - 100 x^{3} + 1 : - 917

Minimum (3, - 917)

Maximum (- 5, 6251), Saddle (0, 1), Minimum (3, - 917)

What is the extreme f(x)=4x^5+10x^4-100x^3+1 ?
The extreme f(x)=4x^5+10x^4-100x^3+1 is Maximum(-5,6251),Saddle(0,1),Minimum(3,-917)