What is the extreme f(x)=3x^5-25x^3+60x ?

The extreme f(x)=3x^5-25x^3+60x is Maximum(-2,-16),Minimum(-1,-38),Maximum(1,38),Minimum(2,16)

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extreme f(x)=3x^5-25x^3+60x

extreme points

f (x) = 3 x^{5} - 25 x^{3} + 60 x

Maximum (- 2, - 16), Minimum (- 1, - 38), Maximum (1, 38), Minimum (2, 16)

Solution steps

f^{'} (x) = 15 x^{4} - 75 x^{2} + 60

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

3 x^{5} - 25 x^{3} + 60 x : - 16

Maximum (- 2, - 16)

Plug

x = - 1

into

3 x^{5} - 25 x^{3} + 60 x : - 38

Minimum (- 1, - 38)

Plug

x = 1

into

3 x^{5} - 25 x^{3} + 60 x : 38

Maximum (1, 38)

Plug

x = 2

into

3 x^{5} - 25 x^{3} + 60 x : 16

Minimum (2, 16)

Maximum (- 2, - 16), Minimum (- 1, - 38), Maximum (1, 38), Minimum (2, 16)

x^{2} + x y + y^{2} - 7 x - 3 y

10 x^{\frac{1}{2}} - x [100]

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

f (x) = (4 x^{2} - 64)^{\frac{1}{5}}

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

What is the extreme f(x)=3x^5-25x^3+60x ?
The extreme f(x)=3x^5-25x^3+60x is Maximum(-2,-16),Minimum(-1,-38),Maximum(1,38),Minimum(2,16)