Is f(x)=sinx concave or convex at x=pi/2?

1 Answer
Oct 24, 2017

See below

Explanation:

to even find concavity, you should know what it means by concave up and concave down.

if a functions f''(x) for a point, like (0.25, 2.25) is positive, like this graph of x^3, but in its 2nd derivative form of 9x

graph{y=9x [-10, 10, -5, 5]}

then its concave-Up

if a functions f''(x) for a point, like (0.2, -0.54) is negative, like the graph of 3x^3+2x+4, which will turn into -27x

graph{-27x [-10, 10, -5, 5]}

then its concave-Down

but all of these points and graphs are linear, your looking for an point on an non-linear graph (sin(x)).

the second derivative of sin(x) is -sin(x)

here's the graph:

graph{-sin(x) [-10, 10, -5, 5]}

at x=pi/2, the point is negative, also known as concave-down. since the graph is going negative at the interval [0, pi]