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1 151 WebCalc Fall 2002-copyright Joe Kahlig In Class Questions MATH 151-Fall 02 October 1 1. The position of a particle is given by the equation s = f (t) = t3 − 6t2 + 9t where t is measured in seconds and s in meters. (a) Find the velocity at time t. (b) What is the velocity after 2 seconds? ds (c) Find and interpret the answer. dt t=4 (d) When is the particle at rest? (e) When is the particle moving in the positive direction? (f) Find the total distance traveled by the particle during the first five seconds. 2. Discuss the derivatives of these functions. 1 − 2x g(x) = f (x) = x2 x for x < −1 for −1 ≤ x ≤ 1 for x > 1 4x2 + 2x + 1 10x − 3 for x < 1 for x ≥ 1 3. Find the values of A and B (if possible) that make k(x) differentiable at x = 1. k(x) = x2 + 2x + 7 for x < 1 Ax + B for x ≥ 1 4. Find the equations of both tangent lines through the point (2, −3) that are tangent to the parabola y = x2 + x.