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

The extreme f(x)=(2x^3)/3+(3x^2)/2-2x is Maximum(-2, 14/3),Minimum(1/2 ,-13/24)

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

extreme points

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

Maximum (- 2, \frac{14}{3}), Minimum (\frac{1}{2}, - \frac{13}{24})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = - 2

into

\frac{2 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 2 x : \frac{14}{3}

Maximum (- 2, \frac{14}{3})

Plug

x = \frac{1}{2}

into

\frac{2 x ^{3}}{3} + \frac{3 x ^{2}}{2} - 2 x : - \frac{13}{24}

Minimum (\frac{1}{2}, - \frac{13}{24})

Maximum (- 2, \frac{14}{3}), Minimum (\frac{1}{2}, - \frac{13}{24})

What is the extreme f(x)=(2x^3)/3+(3x^2)/2-2x ?
The extreme f(x)=(2x^3)/3+(3x^2)/2-2x is Maximum(-2, 14/3),Minimum(1/2 ,-13/24)