What is the extreme 3x^3-2x^2-5x+4 ?

The extreme 3x^3-2x^2-5x+4 is Maximum(-5/9 , 1372/243),Minimum(1,0)

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extreme 3x^3-2x^2-5x+4

extreme points

3 x^{3} - 2 x^{2} - 5 x + 4

Maximum (- \frac{5}{9}, \frac{1372}{243}), Minimum (1, 0)

Solution steps

f^{'} (x) = 9 x^{2} - 4 x - 5

Find intervals:

Increasing

: - \infty < x < - \frac{5}{9},

Decreasing

: - \frac{5}{9} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{5}{9}

into

3 x^{3} - 2 x^{2} - 5 x + 4 : \frac{1372}{243}

Maximum (- \frac{5}{9}, \frac{1372}{243})

Plug

x = 1

into

3 x^{3} - 2 x^{2} - 5 x + 4 : 0

Minimum (1, 0)

Maximum (- \frac{5}{9}, \frac{1372}{243}), Minimum (1, 0)

f (x) = \frac{5 x ^{2} + 20 x + 23}{x ^{2} + 4 x + 5}

\frac{3 - x ^{2}}{x ^{2} - 4}

y = (x + 1)^{2} - 9

f (x) = 3

3 - e^{x}

What is the extreme 3x^3-2x^2-5x+4 ?
The extreme 3x^3-2x^2-5x+4 is Maximum(-5/9 , 1372/243),Minimum(1,0)