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Question

If y=Ax+Bx2, then x2d2ydx2is equal to ?


A

2y

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B

y2

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C

y3

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D

y4

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Solution

The correct option is A

2y


Explanation for the correct option.

Step 1. Find the value of dydx.

Differentiate the function y=Ax+Bx2 with respect to x.

dydx=ddxAx+Bx2=-Ax2+2Bx

Step 2. Find the value of the given expression.

Differentiate the function dydx=-Ax2+2Bx with respect to x.

d2ydx2=ddx-Ax2+2Bx=--2Ax3+2B=2Ax3+B

Now multiply both sides by x2 to get the value of x2d2ydx2.

x2d2ydx2=x2×2Ax3+B=2Ax+Bx2=2y[y=Ax+Bx2]

Hence, the correct option is A.


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