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

##### 1 Answer

Mar 21, 2016

convex at

#### 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 #