JEE Mains · Maths · STD 12 - 6. Application of derivatives
The intercepts on \(x-\) axis made by tangents to the curve \(y = \mathop \smallint \limits_0^x \left| t \right|dt,x \in R\) which is parallel to the line \(y = 2x\) are equal to ::
- A \( \pm 1\)
- B \( \pm 2\)
- C \( \pm 3\)
- D \(\; \pm 4\)
Answer & Solution
Correct Answer
(A) \( \pm 1\)
Step-by-step Solution
Detailed explanation
\(\frac{{dy}}{{dx}} = \left| x \right| = 2\) \(x = \pm 2\) points \(y\int\limits_0^{ \pm 2} {\left| t \right|} dt = \pm 2\) \(\therefore \) equation of tangent is \(y-2=2(x-2)\) or \(y+2=2(x+2)\) \( \Rightarrow \) \(x\)- intercept \(\, = \pm 1\)
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