What is the extreme 3x^4-16x^3+24x^2 ?

The extreme 3x^4-16x^3+24x^2 is Minimum(0,0),Saddle(2,16)

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extreme 3x^4-16x^3+24x^2

extreme points

3 x^{4} - 16 x^{3} + 24 x^{2}

Minimum (0, 0), Saddle (2, 16)

Solution steps

f^{'} (x) = 12 x^{3} - 48 x^{2} + 48 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

3 x^{4} - 16 x^{3} + 24 x^{2} : 0

Minimum (0, 0)

Plug

x = 2

into

3 x^{4} - 16 x^{3} + 24 x^{2} : 16

Saddle (2, 16)

Minimum (0, 0), Saddle (2, 16)

f (x) = \frac{x + 1}{x ^{2} + 1}

x + 3

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

(- 3, 0), (- 7, - 5)

\frac{\frac{x}{2 x ^{2} - 5}}{x}

What is the extreme 3x^4-16x^3+24x^2 ?
The extreme 3x^4-16x^3+24x^2 is Minimum(0,0),Saddle(2,16)