What is the extreme y=-1/2 x^4+4/3 x^3-9 ?

The extreme y=-1/2 x^4+4/3 x^3-9 is Saddle(0,-9),Maximum(2,-19/3)

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extreme y=-1/2 x^4+4/3 x^3-9

extreme points

y = - \frac{1}{2} x^{4} + \frac{4}{3} x^{3} - 9

Saddle (0, - 9), Maximum (2, - \frac{19}{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} - 9 : - 9

Saddle (0, - 9)

Plug

x = 2

into

- \frac{1}{2} x^{4} + \frac{4}{3} x^{3} - 9 : - \frac{19}{3}

Maximum (2, - \frac{19}{3})

Saddle (0, - 9), Maximum (2, - \frac{19}{3})

p er p e n d i c u l a r y + 7 = 1 (x - 3)

cr i t i c a l x^{3} - 4 x^{2} - x + 2

a sy m pt o t es f (x) = \frac{x ^{2}}{x ^{2} - 16}

a sy m pt o t es f (x) = \frac{4}{x}

r an g e f (x) = e^{x - 3}

What is the extreme y=-1/2 x^4+4/3 x^3-9 ?
The extreme y=-1/2 x^4+4/3 x^3-9 is Saddle(0,-9),Maximum(2,-19/3)