Determine two positive numbers whose sum is 30 and whose product is the maximum.

Solution

Let one number = x.
$therefore space space space space space other space number space equals space 30 minus straight x$
$Let space straight P space equals space straight x left parenthesis 30 minus straight x right parenthesis space equals space 30 straight x minus straight x squared space space space space space space space space space space space space space space space rightwards double arrow space space dP over dx equals 30 minus 2 straight x$
$dP over dx space equals space 0 space space gives space us space 30 minus 2 straight x space equals space 0 comma space space space space space space space space space space space space space rightwards double arrow space space straight x space equals space 15 fraction numerator straight d squared straight P over denominator dx squared end fraction space equals space minus 2$
$At space straight x space equals space 15 comma space space space space fraction numerator straight d squared straight P over denominator dx squared end fraction space equals negative 2 space less than space 0 therefore space space space straight P space is space maximum space when space straight x space equals space 15 space space space space rightwards double arrow space space space numbers space are space 15 comma space 30 comma space minus 15 space space straight i. straight e comma space 15 comma space 15$

For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Determine two positive numbers whose sum is 30 and whose product is the maximum.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction