What is the extreme f(x)=3x^5-5x^3+2 ?

The extreme f(x)=3x^5-5x^3+2 is Maximum(-1,4),Saddle(0,2),Minimum(1,0)

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extreme f(x)=3x^5-5x^3+2

extreme points

f (x) = 3 x^{5} - 5 x^{3} + 2

Maximum (- 1, 4), Saddle (0, 2), Minimum (1, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

3 x^{5} - 5 x^{3} + 2 : 4

Maximum (- 1, 4)

Plug

x = 0

into

3 x^{5} - 5 x^{3} + 2 : 2

Saddle (0, 2)

Plug

x = 1

into

3 x^{5} - 5 x^{3} + 2 : 0

Minimum (1, 0)

Maximum (- 1, 4), Saddle (0, 2), Minimum (1, 0)

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

f (x) = x - 1

\frac{x - 7}{x ^{2}}

f (x) = x e^{- 3 x^{2}}

f (x) = 2 x^{2} - 3 x - 1

What is the extreme f(x)=3x^5-5x^3+2 ?
The extreme f(x)=3x^5-5x^3+2 is Maximum(-1,4),Saddle(0,2),Minimum(1,0)