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

The extreme f(x)=(2x^3)/3-(x^2)/2-x is Maximum(-1/2 , 7/24),Minimum(1,-5/6)

Popular >

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

extreme points

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

Maximum (- \frac{1}{2}, \frac{7}{24}), Minimum (1, - \frac{5}{6})

Solution steps

f^{'} (x) = 2 x^{2} - x - 1

Find intervals:

Increasing

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

Decreasing

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

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{2}

into

\frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - x : \frac{7}{24}

Maximum (- \frac{1}{2}, \frac{7}{24})

Plug

x = 1

into

\frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - x : - \frac{5}{6}

Minimum (1, - \frac{5}{6})

Maximum (- \frac{1}{2}, \frac{7}{24}), Minimum (1, - \frac{5}{6})

y = x^{3} - 6 x^{2} + 9 x - 8

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

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

f (x) = \frac{x ^{2} - 24}{x - 5}

f (x) = x e^{- 6 x^{2}}

What is the extreme f(x)=(2x^3)/3-(x^2)/2-x ?
The extreme f(x)=(2x^3)/3-(x^2)/2-x is Maximum(-1/2 , 7/24),Minimum(1,-5/6)