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Find the are of the largest rectangle ...

Find the are of the largest rectangle with lower base on the x-axis and upper vertices on the curve `y=12 -x^(2)`.

A

`20sqrt(2)`

B

`18sqrt(3)`

C

`32`

D

36

Text Solution

Verified by Experts

The correct Answer is:
C
Area `=A=2t (12-t^2)`
`(d A)/(dt)=24-6t^2`.
For maximum value of `A,(d A)/(dt)=0`
`24-6t^2 =0,t= +- 2`
`A=2t(12-t^2)=32` .
.
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