Section 3.6 Activity - The Derivative as a Rate of Change 1. A particle moves along a straight line according to a law of motion given by s(t) = =13 -21 + 2t, where t is given in seconds and s is measured in feet, t20. (a) Find the velocity and acceleration functions at time t. (b) When is the particle at rest? (c) When is the particle moving in the positive direction? (d) When is the particle speeding up? (e) What is the total distance the particle travels in the first 5 seconds? (f) What is the average velocity of the particle over the first 5 seconds? (g) What is the average speed of the particle over the first 5 seconds?2. If the total cost for producing x units of a particular product is given by the function C(x) , then the average cost of production of those x units is given by A(x) = (x) If at a particular company it is known that C(x) =2x3/2 +100x+1500, the find the value of x which minimizes the average cost. What is the minimal average cost? 3. The relationship between the rate of a certain chemical reaction and temperature under certain circumstances is given by R(T) = 0.1(-0.057) +472 +120) grams/sec where R is the rate of reaction and T is the temperature in degrees Celsius. Find the temperature at which the reaction rate reaches its maximum. What is the maximum reaction rate