What is the extreme f(x)=3x^5-20x^3+16 ?

The extreme f(x)=3x^5-20x^3+16 is Maximum(-2,80),Saddle(0,16),Minimum(2,-48)

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extreme f(x)=3x^5-20x^3+16

extreme points

f (x) = 3 x^{5} - 20 x^{3} + 16

Maximum (- 2, 80), Saddle (0, 16), Minimum (2, - 48)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

3 x^{5} - 20 x^{3} + 16 : 80

Maximum (- 2, 80)

Plug

x = 0

into

3 x^{5} - 20 x^{3} + 16 : 16

Saddle (0, 16)

Plug

x = 2

into

3 x^{5} - 20 x^{3} + 16 : - 48

Minimum (2, - 48)

Maximum (- 2, 80), Saddle (0, 16), Minimum (2, - 48)

\frac{x ^{3}}{x - 2}

f (x) = - x^{2} + 4, - 1 \leq x \leq 2

f (x) = 20 x^{3} + 9 x^{2} - 24 x + 12, 0 \leq x \leq 1

5 x^{3} - 30 x^{2} + 45 x

f (x) = - x + 2 cos (x), 0 \leq x \leq 2 π

What is the extreme f(x)=3x^5-20x^3+16 ?
The extreme f(x)=3x^5-20x^3+16 is Maximum(-2,80),Saddle(0,16),Minimum(2,-48)