Question

Is `f(x)=sinx` concave or convex at `x=(3pi)/2`?

Answer 1

convex at `x = (3pi)/2`

Explanation:

To test if a function is concave/convex at f(a), require to find the value of f''(a)

• If f''(a) > 0 then f(x) is convex at x = a

• If f''(a) < 0 then f(x) is concave at x = a

hence f(x) = sinx

f'(x) = cosx

and f''(x) = -sinx

`rArr f''((3pi)/2) = - sin((3pi)/2) = 1`

since f''`((3pi)/2) > 0" then" f(x)" is convex at " x =(3pi)/2`