What is the extreme f(x)=2x^3-11/2 x^2-10x+2 ?

The extreme f(x)=2x^3-11/2 x^2-10x+2 is Maximum(-2/3 , 152/27),Minimum(5/2 ,-209/8)

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extreme f(x)=2x^3-11/2 x^2-10x+2

extreme points

f (x) = 2 x^{3} - \frac{11}{2} x^{2} - 10 x + 2

Maximum (- \frac{2}{3}, \frac{152}{27}), Minimum (\frac{5}{2}, - \frac{209}{8})

Solution steps

f^{'} (x) = 6 x^{2} - 11 x - 10

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < \frac{5}{2},

Increasing

: \frac{5}{2} < x < \infty

Plug

x = - \frac{2}{3}

into

2 x^{3} - \frac{11}{2} x^{2} - 10 x + 2 : \frac{152}{27}

Maximum (- \frac{2}{3}, \frac{152}{27})

Plug

x = \frac{5}{2}

into

2 x^{3} - \frac{11}{2} x^{2} - 10 x + 2 : - \frac{209}{8}

Minimum (\frac{5}{2}, - \frac{209}{8})

Maximum (- \frac{2}{3}, \frac{152}{27}), Minimum (\frac{5}{2}, - \frac{209}{8})

f (x, y) = 8 y^{2} + 5 x^{2} - 10 y + 6 x - 10

f (x) = 8 x^{5} - 120 x^{3} + 43

f (x) = \frac{x ^{2}}{x ^{4} + 1}

f (x) = (8 x)^{3} - (5 x)^{2} - 3 x

f (x) = 2

What is the extreme f(x)=2x^3-11/2 x^2-10x+2 ?
The extreme f(x)=2x^3-11/2 x^2-10x+2 is Maximum(-2/3 , 152/27),Minimum(5/2 ,-209/8)