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Mathematics, 05.11.2019 05:31, nataliamontirl6079
1. (1 pt each) the equation of motion of a particle is s = t 3 − 12t 2 + 36t, t ≥ 0, where s is measured in meters and t is in seconds. (a) find the velocity at time t. (b) what is the velocity after 3 s? (c) when is the particle at rest? (d) when is the particle moving in the positive direction? (e) find the total distance traveled during the first 8 s. (f) find the acceleration at time t and after 3 s. 2. (3 pt each) given p(x) = x n − x, find the intervals over which p(x) is a decreasing function when: (a) n = 2 (b) n = 1 2 (c) n = −1 3. (a) (3 pts) find equations of both lines through the point (2, −3) that are tangent to the parabola y = x 2 + x. (b) (1 pt) show that there is no line through the point (2, 7) that is tangent to the parabola. then sketch a graph to see why. 4. (3 pts) find a cubic function y = ax3+bx2+cx+d whose graph has horizontal tangents at the points (−2, 6) and (2, 0). 5. (a) (3 pts) use the product rule twice to prove that if f, g, and h are differentiable, then (fgh) 0 = f 0 gh + fg0h + fgh0 . (b) (3 pts) use part (a) to differentiate y = x sin x cos x 6. (3 pts)
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1. (1 pt each) the equation of motion of a particle is s = t 3 − 12t 2 + 36t, t ≥ 0, where s is meas...
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