Section 3.5 Activity 1. Write the correct formula for each derivative. (a) d ( sin x) dx ( b ) (cosx ) (c) d (tan x) (d) (csex ) (e) (secx) (f) (cotx) 2. Find the equation of the tangent line to the curve y =4x -6sinx at x = ~ . Leave your answer in exact form and do not use decimal approximations. 3. Let f(x) = 3 .2" cosx . Find f'(x) and f"(x).4. An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass the is pulled downward and then released, it vibrates vertically. The equation of motion is given by s(t) = 4 sin: + 4 cost for t 2 0 , where s is measured in inches and t is measured in seconds. (Take the positive direction to be downward). (a) Find the velocity and acceleration functions at time r. (b) The equilibrium position of the mass is the position at which it is located before it is pulled. Determine at which time the mass first passes through its equilibrium position. (c) How far from the equilibrium position does the mass travel? (d) Determine all values of t for which the mass has a local extreme point on the interval [0, 621']. (e) Find all values of r for which the speed of the mass is the greatest