Is #f(x)=sinx/cosx# concave or convex at #x=0#?

1 Answer
Shwetank Mauria
Mar 20, 2016

It is at a point of inflection.

Explanation:

The function is #f(x)=sinx/cosx=tanx#.

To find out whether it is concave or convex at #x-0#, let us find average of the value of #f(x)# at #x=0+Deltax=Deltax# and #x=0-Deltax=-Deltax#.

Ax #tan(-Deltax)=-tanDeltax#, this should be #0#.

Also #tanx=0# at #x=0#.

Hence, at #x=0#, #f(x)=sinx/cosx=tanx# is neither concave nor convex.

If average of #f(x_0+Deltax))# and #f(x_0-Deltax))# is less than that at #f(x_0)#, it is concave and if average of #f(x_0+Deltax))# and #f(x_0-Deltax))# is less than that at #f(x_0)#, it is convex. If they are equal it is point of inflection.

It is at a point of inflection.

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