Question

Find the points on the curve y = (cosx – 1) in [0, 2π], where the tangent is parallel to x-axis

Answer 1

We have y = cosx – 1

∴ `"dy"/"dx"` = – sin x

For tangent to be parallel to x-axis

We must have `"dy"/"dx"` = 0

∴ – sin x = 0

∴ x = π ∈ [0, 2π]

y(π) = cos π – 1 = –2

Hence, the required point on the curve, where the tangent drawn is parallel to the x-axis is (π, –2)