What is the extreme-x^2+3x-2,1<= x<= 3 ?

The extreme-x^2+3x-2,1<= x<= 3 is Minimum(1,0),Maximum(3/2 , 1/4),Minimum(3,-2)

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extreme-x^2+3x-2,1<= x<= 3

extreme points

- x^{2} + 3 x - 2, 1 \leq x \leq 3

Minimum (1, 0), Maximum (\frac{3}{2}, \frac{1}{4}), Minimum (3, - 2)

Solution steps

Find the critical points:

x = 1, x = \frac{3}{2}, x = 3

Domain of

- x^{2} + 3 x - 2, 1 \leq x \leq 3 : 1 \leq x \leq 3

Find intervals:

Increasing

: 1 < x < \frac{3}{2},

Decreasing

: \frac{3}{2} < x < 3

Plug the extreme point

x = 1

into

- x^{2} + 3 x - 2 \Rightarrow y = 0

Minimum (1, 0)

Plug the extreme point

x = \frac{3}{2}

into

- x^{2} + 3 x - 2 \Rightarrow y = \frac{1}{4}

Maximum (\frac{3}{2}, \frac{1}{4})

Plug the extreme point

x = 3

into

- x^{2} + 3 x - 2 \Rightarrow y = - 2

Minimum (3, - 2)

Minimum (1, 0), Maximum (\frac{3}{2}, \frac{1}{4}), Minimum (3, - 2)

\frac{2 x - x ^{2}}{x}

f (x) = x^{2}, - 2 \leq x \leq 1

f (x) = \frac{x ^{2} - 27}{x - 6}

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

f (x, y) = y^{3} - 3 y x^{2} - 3 y^{2} - 3 x^{2} + 1

What is the extreme-x^2+3x-2,1<= x<= 3 ?
The extreme-x^2+3x-2,1<= x<= 3 is Minimum(1,0),Maximum(3/2 , 1/4),Minimum(3,-2)