What is the extreme y= 1/3 x^3-5/2 x^2+6x-2 ?

The extreme y= 1/3 x^3-5/2 x^2+6x-2 is Maximum(2, 8/3),Minimum(3, 5/2)

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extreme y= 1/3 x^3-5/2 x^2+6x-2

extreme points

y = \frac{1}{3} x^{3} - \frac{5}{2} x^{2} + 6 x - 2

Maximum (2, \frac{8}{3}), Minimum (3, \frac{5}{2})

Solution steps

f^{'} (x) = x^{2} - 5 x + 6

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 2

into

\frac{1}{3} x^{3} - \frac{5}{2} x^{2} + 6 x - 2 : \frac{8}{3}

Maximum (2, \frac{8}{3})

Plug

x = 3

into

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

Minimum (3, \frac{5}{2})

Maximum (2, \frac{8}{3}), Minimum (3, \frac{5}{2})

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

f (x) = 6 + 12 x - 3 x^{2}

f (x) = e^{x^{2} - 9}

f (x) = 5 y e^{x} - 6 e^{y}

f (x) = x_{2} - 4 \cdot 2 - 4 x

What is the extreme y= 1/3 x^3-5/2 x^2+6x-2 ?
The extreme y= 1/3 x^3-5/2 x^2+6x-2 is Maximum(2, 8/3),Minimum(3, 5/2)