Math 241 Question 1. (12 points) Midterm 2 - Page 2 of 9 S A 'ua'u...

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Math 241 Question 1. (12 points) Midterm 2 - Page 2 of 9 S A 'ua'u is walking along a cliff-edge (which is a straight line) looking for some dinner. It's positions at time t is given by the graph below. Number of questions: 8 m 4 8 t (a) During the interval from t=0 to t = 2, is the 'ua'u speeding up, slowing down, or neither? State what properties of the first / second derivatives of s(t) this corresponds to. (b) Give the values of t (if there are any) when the 'ua'u changes its direction of motion. (c) The graph has an inflection point at t=5. Use this to describe the motion of the 'ua'u during the interval from t = 4 to t = 6. (d) On what intervals of t (if any) is the 'ua'u moving at a constant speed? What conditions on the first / second derivatives of s(t) are necessary for this to occur? Math 241 Question 1. (12 points) Midterm 2 - Page 2 of 9 S A 'ua'u is walking along a cliff-edge (which is a straight line) looking for some dinner. It's positions at time t is given by the graph below. Number of questions: 8 m 4 8 t (a) During the interval from t=0 to t = 2, is the 'ua'u speeding up, slowing down, or neither? State what properties of the first / second derivatives of s(t) this corresponds to. (b) Give the values of t (if there are any) when the 'ua'u changes its direction of motion. (c) The graph has an inflection point at t=5. Use this to describe the motion of the 'ua'u during the interval from t = 4 to t = 6. (d) On what intervals of t (if any) is the 'ua'u moving at a constant speed? What conditions on the first / second derivatives of s(t) are necessary for this to occur?

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