• If z'(x)= 3+52, what is z(x)? • If qq' = √²+1, what is q(x)? • Let f(t) = teat+b, where a ‡ 0 and b are constant coefficients and t > 0. (a) Find a and b such that f(t) has a critical point at t = 2. (b) Continue from (a), find b such that f= 3 at the critical point. (c) Finally, determine the behavior of f(t) as t → [infinity] with a and b from above. (d) With a and b from (b), sketch f(t) for t € [0, 10]. • Let g(t) = sin teat+ ß, with a 0 and 3 constant coefficients. Find the conditions on a and 3 such that there is more than one critical point for g(t). Find the expression for the critical points in terms of a and 3. Let y(t) = 5e to cos(wot) for t > 0. (a) Sketch y(t) for t = [0, 10] if the oscillation frequency wo 27 per second (Hertz). (b) If y(4) = 0, what can one say about the frequency wo? (c) The function y(t) has a time-varying oscillation amplitude 5e to. Find the time T when this time-dependent amplitude first decreases to less than 1.