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 #
