What is the extreme f(x)=-x^2+5x-6,2<= x<= 3 ?

The extreme f(x)=-x^2+5x-6,2<= x<= 3 is Minimum(2,0),Maximum(5/2 , 1/4),Minimum(3,0)

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extreme f(x)=-x^2+5x-6,2<= x<= 3

extreme points

f (x) = - x^{2} + 5 x - 6, 2 \leq x \leq 3

Minimum (2, 0), Maximum (\frac{5}{2}, \frac{1}{4}), Minimum (3, 0)

Solution steps

Find the critical points:

x = 2, x = \frac{5}{2}, x = 3

Domain of

- x^{2} + 5 x - 6, 2 \leq x \leq 3 : 2 \leq x \leq 3

Find intervals:

Increasing

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

Decreasing

: \frac{5}{2} < x < 3

Plug the extreme point

x = 2

into

- x^{2} + 5 x - 6 \Rightarrow y = 0

Minimum (2, 0)

Plug the extreme point

x = \frac{5}{2}

into

- x^{2} + 5 x - 6 \Rightarrow y = \frac{1}{4}

Maximum (\frac{5}{2}, \frac{1}{4})

Plug the extreme point

x = 3

into

- x^{2} + 5 x - 6 \Rightarrow y = 0

Minimum (3, 0)

Minimum (2, 0), Maximum (\frac{5}{2}, \frac{1}{4}), Minimum (3, 0)

f (x, y) = x^{3} - y^{2} - 6 x y - 4

f (x) = x^{2} - 6 x + 9

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

f (x) = 3 (x - 4)^{\frac{2}{3}} + 6

f (x) = - 4 cos (3 x) - 4, (0, 2 π)

What is the extreme f(x)=-x^2+5x-6,2<= x<= 3 ?
The extreme f(x)=-x^2+5x-6,2<= x<= 3 is Minimum(2,0),Maximum(5/2 , 1/4),Minimum(3,0)