2.5/2.7 Questions Problem 1. Explain how you know when to use the power rule, product rule, quotient rule, and chain rule to calculate derivatives. What do functions look like that require each of these rules? Be specic! Problem 2. Let ax) = sinzc and 9(32) = $3. (a) Find h(m) = f (g(m)) and calculate h'(9:). (b) Find 16(3)) = g( f (56)) and calculate k'(a:). Problem 3. Find the derivatives of the following functions. (a) g(x) = (5x - 8) (2+4) = 20 + 4 5 x - 8 Two methods: (1)product+chain rule or (2) quotient rule-pros/cons? (b) h(x) = sin (x2 + 5x) (c) f(x) = sec(V 4x + 1) (d) g(x) = V2x2 + 5x + 4 (e) p(x) = sin(x2 cosx)Problem 4. Particle motion is described by several phrases that are very similar, but have important differences. Work with your classmates to compare and contrast the following phrases and to describe the difference: (a) \"the particle has a speed of 5 m/s\" vs. \"the particle has a velocity of 5 m/s\" (b) \"the particle is speeding up\" vs. \"the particle has positive acceleration\" (c) \"displacement\" vs. \"total distance traveled\" Problem 5. The graph to the right shows the velocity v(t) of a particle Ineving on a horizontal coordinate line (in m/s). Use this graph to answer the following questions. Your answers should be in interval notation. (a) When is the particle moving in the positive / negative direction? (b) What is the particle's maximum speed? velocity? (c) When is the particle motionless? (f) At t = 9 the Particle: (circle all that apply) I. is moving in the positive direction II. is m0ving in the negative direction (d) When is the acceleration positive? Negative? 111' 15 speeding up . is slowing dawn . has positive acceleration S 0. Then do so, to end up with an expression involving f ' " (9:). Hint: your answer should be the same as the formula from part 2