What is the extreme-1/2 x^4+4/3 x^3-14 ?

The extreme-1/2 x^4+4/3 x^3-14 is Saddle(0,-14),Maximum(2,-34/3)

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extreme-1/2 x^4+4/3 x^3-14

extreme points

- \frac{1}{2} x^{4} + \frac{4}{3} x^{3} - 14

Saddle (0, - 14), Maximum (2, - \frac{34}{3})

Solution steps

f^{'} (x) = - 2 x^{3} + 4 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

- \frac{1}{2} x^{4} + \frac{4}{3} x^{3} - 14 : - 14

Saddle (0, - 14)

Plug

x = 2

into

- \frac{1}{2} x^{4} + \frac{4}{3} x^{3} - 14 : - \frac{34}{3}

Maximum (2, - \frac{34}{3})

Saddle (0, - 14), Maximum (2, - \frac{34}{3})

f (x, y) = 2 x y - 32 x + 64 y

f (x) = 6 x y - \frac{1}{2} (x^{4} + y^{4}) - 2

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

f (x) = x^{4} - 2 x^{2} + y^{3} - 27 y - 15

f (x) = 0.01 x^{2} - 0.2 x + 8

What is the extreme-1/2 x^4+4/3 x^3-14 ?
The extreme-1/2 x^4+4/3 x^3-14 is Saddle(0,-14),Maximum(2,-34/3)