What is the extreme x^5-15x^3+3 ?

The extreme x^5-15x^3+3 is Maximum(-3,165),Saddle(0,3),Minimum(3,-159)

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extreme x^5-15x^3+3

extreme

Maximum (- 3, 165), Saddle (0, 3), Minimum (3, - 159)

Solution steps

f^{'} (x) = 5 x^{4} - 45 x^{2}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

x^{5} - 15 x^{3} + 3 : 165

Maximum (- 3, 165)

Plug

x = 0

into

x^{5} - 15 x^{3} + 3 : 3

Saddle (0, 3)

Plug

x = 3

into

x^{5} - 15 x^{3} + 3 : - 159

Minimum (3, - 159)

Maximum (- 3, 165), Saddle (0, 3), Minimum (3, - 159)

What is the extreme x^5-15x^3+3 ?
The extreme x^5-15x^3+3 is Maximum(-3,165),Saddle(0,3),Minimum(3,-159)