What is the extreme f(x)=3x^5-25x^3+60x+1 ?

The extreme f(x)=3x^5-25x^3+60x+1 is Maximum(-2,-15),Minimum(-1,-37),Maximum(1,39),Minimum(2,17)

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extreme f(x)=3x^5-25x^3+60x+1

extreme

Maximum (- 2, - 15), Minimum (- 1, - 37), Maximum (1, 39), Minimum (2, 17)

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 + 1 : - 15

Maximum (- 2, - 15)

Plug

x = - 1

into

3 x^{5} - 25 x^{3} + 60 x + 1 : - 37

Minimum (- 1, - 37)

Plug

x = 1

into

3 x^{5} - 25 x^{3} + 60 x + 1 : 39

Maximum (1, 39)

Plug

x = 2

into

3 x^{5} - 25 x^{3} + 60 x + 1 : 17

Minimum (2, 17)

Maximum (- 2, - 15), Minimum (- 1, - 37), Maximum (1, 39), Minimum (2, 17)

What is the extreme f(x)=3x^5-25x^3+60x+1 ?
The extreme f(x)=3x^5-25x^3+60x+1 is Maximum(-2,-15),Minimum(-1,-37),Maximum(1,39),Minimum(2,17)