Question

The length and width of a rectangle must have a sum of 30. Find the dimensions of the rectangle that will have the maximum area. [hint: let x and 30-x be the length and width] the area can be described by the function f(x)=x(30-x).]

Answer 1

Date: Page No: Now esa 50%->(2 ) 30-2D enve

Answer 2

SOLUTION :

Let the length be x .

So, width = 30 - x

A = x(30 - x) = 30x - x^2

For maximum area, dA/dx = 0 and d2A/dx2 = negative

So,

dA/dx = 0 and d2A/dx2 should be negative

=> 30 - 2x = 0. And d2A/dx2 = - 2x

=> x = 15 ans at x = 15, d2A/dx2 = - 2 * 15 = - 30 (negative)

Hence, maximum area will occur when length = 15 and width = 15 (ANSWER).