Q. 71

Find the points on the curve y = (cosx – 1) in [0, ], where the tangent is parallel to x-axis.

Answer :

Given: Equation of curve, y = cos x – 1

Firstly, we differentiate the above equation with respect to x, we get





Given tangent to the curve is parallel to the x – axis


This means, Slope of tangent = Slope of x – axis



- sin x = 0


sin x = 0


x = sin-1(0)


x = π (0, 2π)


Put x = π in y = cos x – 1, we have


y = cos π – 1 = -1 – 1 = -2 [ cos π = -1]


Hence, the tangent to the curve is parallel to the x –axis at


(π, -2)


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