What is the extreme f(x)=3x^5-45x^3 ?

The extreme f(x)=3x^5-45x^3 is Maximum(-3,486),Saddle(0,0),Minimum(3,-486)

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extreme f(x)=3x^5-45x^3

extreme points

f (x) = 3 x^{5} - 45 x^{3}

Maximum (- 3, 486), Saddle (0, 0), Minimum (3, - 486)

Solution steps

f^{'} (x) = 15 x^{4} - 135 x^{2}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

3 x^{5} - 45 x^{3} : 486

Maximum (- 3, 486)

Plug

x = 0

into

3 x^{5} - 45 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

3 x^{5} - 45 x^{3} : - 486

Minimum (3, - 486)

Maximum (- 3, 486), Saddle (0, 0), Minimum (3, - 486)

x (x + 1) (x + 2) (x + 3)

y = x + 2 cos (x), 0 \leq x \leq 2 π

f (x, y) = y^{3} - x^{3} - 2 x y + 6

f (x) = x^{3} - 3 x^{2} - 9 x + 12

f (x) = 20 x^{3} + 9 x^{2} - 24 x + 12, (0, 1)

What is the extreme f(x)=3x^5-45x^3 ?
The extreme f(x)=3x^5-45x^3 is Maximum(-3,486),Saddle(0,0),Minimum(3,-486)