Verified answer

Rewrite as sine wave with amplitude A and phase u:

f(t) = 3sin(t) + cos(t) = A sin( t + u ) = A sin(t) cos(u) + A cos(t) sin(u)

So A cos(u) = 3 and A sin(u) = 1

(3/A)^2 + (1/A)^2 = 1, hence A = sqrt(10) is the maximum value