Question

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

Answer 1

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.. .