Q. 71

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

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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