What is the extreme f(z)=z+z^3-2z^2-4 ?

The extreme f(z)=z+z^3-2z^2-4 is Maximum(1/3 ,-104/27),Minimum(1,-4)

extreme f(z)=z+z^3-2z^2-4

extreme points

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

Maximum (\frac{1}{3}, - \frac{104}{27}), Minimum (1, - 4)

Solution steps

f^{'} (z) = 3 z^{2} - 4 z + 1

Find intervals:

Increasing

: - \infty < z < \frac{1}{3},

Decreasing

: \frac{1}{3} < z < 1,

Increasing

: 1 < z < \infty

Plug

z = \frac{1}{3}

into

z + z^{3} - 2 z^{2} - 4 : - \frac{104}{27}

Maximum (\frac{1}{3}, - \frac{104}{27})

Plug

z = 1

into

z + z^{3} - 2 z^{2} - 4 : - 4

Minimum (1, - 4)

Maximum (\frac{1}{3}, - \frac{104}{27}), Minimum (1, - 4)

f (x) = 1 + \frac{1}{x} + \frac{5}{x ^{2}} + \frac{1}{x ^{3}}

f (x) = \frac{x ^{2} - 0.8 x + 0.32}{1.6 - 2 x}

f (x) = 3 x^{2} - 9 x + 9 x y^{2}

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

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

What is the extreme f(z)=z+z^3-2z^2-4 ?
The extreme f(z)=z+z^3-2z^2-4 is Maximum(1/3 ,-104/27),Minimum(1,-4)