The intercepts on x‑axis made by tangents to the curve, , which are parallel to the line y = 2x are equal to :

Engineering

Mathematics

Tangent and Normal

Question

The intercepts on x‑axis made by tangents to the curve, $y = \int_{0}^{x} | t | dt, x \in R$ , which are parallel to the line y = 2x are equal to :

± 3

± 2

± 1

± 4

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$y = \frac{- x^{2}}{2}$ if x < 0

$y = \frac{x^{2}}{2}$ if x $\geq$ 0

$\frac{dy}{dx} = - x$ x < 0

$\frac{dy}{dx} = x$ x $\geq$ 0

for slope = 2, x = ± 2

$∴$ point of tangency (2, 2) (–2, – 2) equation of tangent

(y – (± 2)) = 2(x – (± 2))

for y = 0, x = ± 1

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