JEE Main 2013MathematicsApplication of DerivativesHardMCQ

JEE Main 2013 — Application of Derivatives Question with Solution

JEE Main 2013 (07 Apr)

Question

The intercepts on the x-axis made by tangents to the curve, y=∫0xt dt, x∈R, which are parallel to the line y=2x, are equal to 

Choose an option

Show full solutionCorrect option: C
Correct answer
C ± 1

Step-by-step explanation

Given y=∫0xtdt

If x>0, then

y=∫0xtdt
⇒y=x22

Ff x<0, then y=− x 2 2

∴ y={x2/2,x>0-x2/2,x<0

Now, dydx={x,x>0-x,x<0

Slope of tangent =2

Hence x=2, y=2 or x=-2, y=-2

Eq. of tangent y=2x-2 or y=2x+2

Hence, x-intercept =1 or -1.
 

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About this question

This is a previous-year question from JEE Main 2013, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.