What is the extreme f(x)=3x^3-6x^2-5x+1 ?

The extreme f(x)=3x^3-6x^2-5x+1 is Maximum(-1/3 , 17/9),Minimum(5/3 ,-91/9)

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extreme f(x)=3x^3-6x^2-5x+1

extreme points

f (x) = 3 x^{3} - 6 x^{2} - 5 x + 1

Maximum (- \frac{1}{3}, \frac{17}{9}), Minimum (\frac{5}{3}, - \frac{91}{9})

Solution steps

f^{'} (x) = 9 x^{2} - 12 x - 5

Find intervals:

Increasing

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

Decreasing

: - \frac{1}{3} < x < \frac{5}{3},

Increasing

: \frac{5}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

3 x^{3} - 6 x^{2} - 5 x + 1 : \frac{17}{9}

Maximum (- \frac{1}{3}, \frac{17}{9})

Plug

x = \frac{5}{3}

into

3 x^{3} - 6 x^{2} - 5 x + 1 : - \frac{91}{9}

Minimum (\frac{5}{3}, - \frac{91}{9})

Maximum (- \frac{1}{3}, \frac{17}{9}), Minimum (\frac{5}{3}, - \frac{91}{9})

- x^{3} + 3 x^{2} - 2

f (x, y) = 8 x^{3} - 24 x y + y^{3}

f (x) = e^{x^{2}}

f (x, y) = 3 x - 2 y - \frac{( x y + 2 ) ^{2}}{x} + y - 2

f (x) = x^{3} - 12 x^{2} + 45 x + 8

What is the extreme f(x)=3x^3-6x^2-5x+1 ?
The extreme f(x)=3x^3-6x^2-5x+1 is Maximum(-1/3 , 17/9),Minimum(5/3 ,-91/9)