What is the extreme y=x^5-15x^3+100 ?

The extreme y=x^5-15x^3+100 is Maximum(-3,262),Saddle(0,100),Minimum(3,-62)

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extreme y=x^5-15x^3+100

extreme points

y = x^{5} - 15 x^{3} + 100

Maximum (- 3, 262), Saddle (0, 100), Minimum (3, - 62)

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} + 100 : 262

Maximum (- 3, 262)

Plug

x = 0

into

x^{5} - 15 x^{3} + 100 : 100

Saddle (0, 100)

Plug

x = 3

into

x^{5} - 15 x^{3} + 100 : - 62

Minimum (3, - 62)

Maximum (- 3, 262), Saddle (0, 100), Minimum (3, - 62)

f (x) = (ln (x^{2} + 1))

f (x) = 3 x + 5 x^{- 1}

f (x) = (x - 1)^{5}

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

f (x) = x^{2} = - 4 a y

What is the extreme y=x^5-15x^3+100 ?
The extreme y=x^5-15x^3+100 is Maximum(-3,262),Saddle(0,100),Minimum(3,-62)