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Application Of Derivatives

Question
CBSEENMA12035486
Wired Faculty App

Amongst all pairs of positive numbers with product 64, find those whose sum is the least.

Solution

Let straight x comma space 64 over straight x be the two numbers
Let space straight S space equals space straight x plus 64 over straight x space space space space rightwards double arrow space space space dS over dx space equals space 1 minus 64 over straight x squared
dS over dx space equals 0 space space gives space us space 1 minus 64 over straight x squared space equals space 0 comma
therefore space space space space straight x squared minus 64 space equals space 0 space space space space space rightwards double arrow space space space space straight x squared space equals space 64 comma space space space space space space rightwards double arrow space space straight x space equals space 8 comma space space minus 8 Rejecting space straight x space equals space minus 8 space left parenthesis as space numbers space are space plus ve right parenthesis space we space get space straight x space equals space 8 space space space space space space space space space space space space space space space space space space space space space fraction numerator straight d squared straight S over denominator dx squared end fraction space equals space 128 over straight x cubed At space space space space straight x space equals 8 comma space space space space space fraction numerator straight d squared straight S over denominator dx squared end fraction space equals space fraction numerator 128 over denominator left parenthesis 8 right parenthesis cubed end fraction space equals space 1 fourth greater than 0 therefore space space space space straight S space is space minimum space when space straight x space equals space 8 therefore space space space space numbers space are space 8 comma space 64 over 8 space space or space space 8 comma space 8

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.

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