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

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

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

extreme points

y = - x^{2} + 1 -, 1 \leq x \leq 2

Maximum (1, -), Minimum (2, - 3)

Solution steps

Find the critical points:

x = 1, x = 2

Domain of

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

Find intervals:

Decreasing

: 1 < x < 2

Plug the extreme point

x = 1

into

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

Maximum (1, -)

Plug the extreme point

x = 2

into

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

Minimum (2, - 3)

Maximum (1, -), Minimum (2, - 3)

f (x) = 3 x^{4} - 12 x^{3} - 60 x^{2} + 4

f (x) = 13 e^{- x}

f (x) = - x^{4} - 6 x

P (X, Y) = 36 X^{2} - 9 Y^{2}

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

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