What is the extreme f(x)= 5/3 x^3-65/2 x^2+200x-1 ?

The extreme f(x)= 5/3 x^3-65/2 x^2+200x-1 is Maximum(5, 2369/6),Minimum(8, 1117/3)

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extreme f(x)= 5/3 x^3-65/2 x^2+200x-1

extreme points

f (x) = \frac{5}{3} x^{3} - \frac{65}{2} x^{2} + 200 x - 1

Maximum (5, \frac{2369}{6}), Minimum (8, \frac{1117}{3})

Solution steps

f^{'} (x) = 5 x^{2} - 65 x + 200

Find intervals:

Increasing

: - \infty < x < 5,

Decreasing

: 5 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = 5

into

\frac{5}{3} x^{3} - \frac{65}{2} x^{2} + 200 x - 1 : \frac{2369}{6}

Maximum (5, \frac{2369}{6})

Plug

x = 8

into

\frac{5}{3} x^{3} - \frac{65}{2} x^{2} + 200 x - 1 : \frac{1117}{3}

Minimum (8, \frac{1117}{3})

Maximum (5, \frac{2369}{6}), Minimum (8, \frac{1117}{3})

f (x) = 4 x^{2} e^{- 0.25 x}

f (x) = x^{3} - 9 x^{2} + 15 x + 2

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

f (x) = - \frac{2}{3} x^{3} + 9 x^{2} - 28 x + 1

f (x) = ln (x^{2} + 4)

What is the extreme f(x)= 5/3 x^3-65/2 x^2+200x-1 ?
The extreme f(x)= 5/3 x^3-65/2 x^2+200x-1 is Maximum(5, 2369/6),Minimum(8, 1117/3)