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Find the point on the curve y = cos x – 1, x [π2,3π2] at which tangent is parallel to the x-axis.

Solution :

Let f(x) = cos x – 1, Clearly f(x) is continous on [π2,3π2] and differentiable on (π2,3π2).

Also, f(π2) = cosπ2 – 1 = -1 = f(3π2).

Thus, all the conditions of rolle’s theorem are satisfied. Consequently,there exist at least one point c (π2,3π2) for which f'(c) = 0. But,

f'(c) = 0   -sin c = 0    c = π

   f(c) = cos \pi – 1 = -2

By the geometric interpretation of rolle’s theorem (\pi, -2) is the point on y = cos x – 1 where tangent is parallel to x-axis.


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