Mathematics: What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 3 − x2?

Yes it does. The opposite sides are parallel....

What is the area of the largest rectangle with

majailaharris200

10.03.2022

Step-by-step explanation:

Let us first construct a rectangle ABCD, in which A is the point at lower right hand corner and B,C,D are the points marked according to A,

Now, let A= (p,0)

B= (-p,0) ,

C= $(-p,3-p^{2})$

and D= $(p,3-p^{2})$

Then the area of rectangle is given as: BA×AD

= $(2p)(3-p^{2})$

A= $6p-2p^{3}$

Taking the derivative with respect to p, we have

$A^{'}$ = $6-6p^{2}$

Now, $A^{'}$ =0

⇒ $6-6p^{2}$ =0

⇒ $6p^{2}=6$

⇒ $p^{2}=1$

Since, wehav eto find the greater area, therefore we will take p=1.

Now, substituting the value of p in (A), we have

Greater area= A= 6-2(1) = 4 sq units

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