99 Percentile Qs Bank for JEE MainMathematicsApplication of Derivatives

Divide 10 into two parts such that the sum of double of the first and the square of the second is minimum

Options

A(6,4)
B(7,3)
C(8,2)
D(9,1)

Correct answer

D. (9,1)

Step-by-step solution

Let x and y be the two parts of the number 10 . +y=10 (i) According to the question, Let aligned A &=2 x+y² &=2 x+(10-x)² &=2 x+100+x²-20 x &=x²-18 x+100 aligned On differentiating w.r.t. x , we get d A d x =2 x-18 For max or min of A , Put d A d x =0=2 x-18 =9 Now, d² A d x² =2>0 ( ) On putting x=9 in Eq. (i), we get y=1 (x, y)=(9,1)

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