What is the extreme 4x^3+7x^2-20x+9 ?

The extreme 4x^3+7x^2-20x+9 is Maximum(-2,45),Minimum(5/6 ,-53/108)

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extreme 4x^3+7x^2-20x+9

extreme points

4 x^{3} + 7 x^{2} - 20 x + 9

Maximum (- 2, 45), Minimum (\frac{5}{6}, - \frac{53}{108})

Solution steps

f^{'} (x) = 12 x^{2} + 14 x - 20

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < \frac{5}{6},

Increasing

: \frac{5}{6} < x < \infty

Plug

x = - 2

into

4 x^{3} + 7 x^{2} - 20 x + 9 : 45

Maximum (- 2, 45)

Plug

x = \frac{5}{6}

into

4 x^{3} + 7 x^{2} - 20 x + 9 : - \frac{53}{108}

Minimum (\frac{5}{6}, - \frac{53}{108})

Maximum (- 2, 45), Minimum (\frac{5}{6}, - \frac{53}{108})

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

3 x^{7} - x^{5} - 7 x^{4} - 2 x^{3} + 3 x^{2}

2 x + 4 - 1

x + 3 y = 9

f (x) = 3 x^{2} + 2 y^{2} = 48

What is the extreme 4x^3+7x^2-20x+9 ?
The extreme 4x^3+7x^2-20x+9 is Maximum(-2,45),Minimum(5/6 ,-53/108)