What is the extreme f(x)=(x^3)/3-(x^2)/4-5x+5 ?

The extreme f(x)=(x^3)/3-(x^2)/4-5x+5 is Maximum(-2, 34/3),Minimum(5/2 ,-185/48)

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extreme f(x)=(x^3)/3-(x^2)/4-5x+5

extreme points

f (x) = \frac{x ^{3}}{3} - \frac{x ^{2}}{4} - 5 x + 5

Maximum (- 2, \frac{34}{3}), Minimum (\frac{5}{2}, - \frac{185}{48})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

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

Increasing

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

Plug

x = - 2

into

\frac{x ^{3}}{3} - \frac{x ^{2}}{4} - 5 x + 5 : \frac{34}{3}

Maximum (- 2, \frac{34}{3})

Plug

x = \frac{5}{2}

into

\frac{x ^{3}}{3} - \frac{x ^{2}}{4} - 5 x + 5 : - \frac{185}{48}

Minimum (\frac{5}{2}, - \frac{185}{48})

Maximum (- 2, \frac{34}{3}), Minimum (\frac{5}{2}, - \frac{185}{48})

f (x) = 6 x^{3} + x^{2} - 2

f (x, y) = x^{2} - 4 x y + 5 y^{2} + 2 x + 4 y - 4

f (x) = 1 + \frac{1}{x} + \frac{9}{x ^{2}} + \frac{1}{x ^{3}}

f (x, y) = x^{3} - 3 x + y^{2} - 4 y

0.0025 x^{4} + 0.5 x^{3} - 8 x^{2} + 1000

What is the extreme f(x)=(x^3)/3-(x^2)/4-5x+5 ?
The extreme f(x)=(x^3)/3-(x^2)/4-5x+5 is Maximum(-2, 34/3),Minimum(5/2 ,-185/48)