1. Consider the function f(t)=,_,;(2t, 03t 0. In the lectures, we showed that t* is a critical point of the function f. (a) Without using an explicit formula for r(t), compute f\"(t*) and show that if the graph of r(t) is always concave downwards, then, by the Second Derivative Test, f (t) attains a local maximum value at t = 15*. (b) Now suppose r(t) has an explicit formula t t+a where ,u and a are positive constants (parameters of the model). Show that there is precisely one value t = t* such that f has a critical point at t*, nd a formula for t* in terms of the model parameters To, .11, a and prove by examining the signs of f'(t) for all t that f (15*) is a global maximum value. 'r(t) = n , OSt