What is the extreme f(x)=4x^5-60x^3 ?

The extreme f(x)=4x^5-60x^3 is Maximum(-3,648),Saddle(0,0),Minimum(3,-648)

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extreme f(x)=4x^5-60x^3

extreme points

f (x) = 4 x^{5} - 60 x^{3}

Maximum (- 3, 648), Saddle (0, 0), Minimum (3, - 648)

Solution steps

f^{'} (x) = 20 x^{4} - 180 x^{2}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

4 x^{5} - 60 x^{3} : 648

Maximum (- 3, 648)

Plug

x = 0

into

4 x^{5} - 60 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

4 x^{5} - 60 x^{3} : - 648

Minimum (3, - 648)

Maximum (- 3, 648), Saddle (0, 0), Minimum (3, - 648)

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

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

3 x^{2} - 18 x + 15

2 x^{3} - 3 x^{2} - 12 x + 18

f (x) = e^{- x^{6}}, - 2 \leq x \leq 1

What is the extreme f(x)=4x^5-60x^3 ?
The extreme f(x)=4x^5-60x^3 is Maximum(-3,648),Saddle(0,0),Minimum(3,-648)