Is #f(x) =sinx/x# concave or convex at #x=1#?

1 Answer
A. S. Adikesavan
Mar 11, 2016

Concave..

Explanation:

Here, the angular measure x, in sin x, is in #radian#. This has to be emphasized in every Calculus class, by every teacher.

Differentiate twice with respect to x.
The second derivative at x = 1 is #sin 1 - 2 cos 1 < 0.
The first derivative is a decreasing function, at x = 1.

AS x increases, the tangent rotates in the clockwise sense, The curve is concave.. .

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