1.

Find the maximum or minimum values of the function. `y=9-(x-3)^(2)`

Answer» `y=9-(x-3)^(2) = 6x-x^(2)`
`(dy)/(dx)=6-2x`
For minimum or maximum value of y,
`(dy)/(dx)=0`
`rArr "" 6-2x=0 "" rArr "" x=3`
Here `(d^(2)y)/(dx^(2))=-2` is less than zero at x=3.
`y_(max)=9-(3-3)^(2)=9`


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