MTE 494 04/20/10Average Speed/Rates of Change1. State the meaning of constant speed that we have publicly agreed to use.An object is moving at a constant speed (distance with respect to time) if and only if:2. State the meaning of average speed that we have publicly agreed to use.3. Extend the above meaning of average speed to average rate of change of one quantity with respect to another.4. A spherical tank in a microbrewery is being filled with water. The supervisor records the amount (volume) of water in the tank and the water's depth in the tank at two moments in time. At 2.72 feet there were 99.35 gallons of water in the tank. At 4.35 feet there were 175.72 gallons of water in the tank. What was the average rate of change of volume with respect to height over this interval of height? Explain what this number means.1MTE 494 04/20/105. The idea of average rate of change involves thinking of a hypothetical or “fictitious” scenario. What role such a scenario play in making the idea of average rate of change sensible?6. When an object falls from a resting start, the distance (in feet) it has fallen x seconds after being released is given by the function d(x) = 16x2 (assuming no air resistance).a) Consider the function g(x) = d(x + 1.2) - d(x), for d as given above.(i) Graph the function g. (ii) What does 1.2 represent? What does the point (0.7, g(0.7)) represent? (iii) What does each point on the graph of g represent?(iv) What question would the graph of g answer?b) Consider the function h(x) = d(x + .01) - d(x), for d as given above.(i) Graph the function h. (ii) What does .01 represent? (iii) What does the point (0.7, h(0.7)) represent? (iv) What does each point on the graph of h represent?c) Consider the function , for d as given above.(i) Graph the function k. (ii) What does 1.5 represent? (iii) What does each point on the graph of k represent? Give an example.d) Consider the function , where h is a parameter that varies over the interval (0.1, 10). (i) Anticipate what the graph of m will be. (ii) What does h represent? (iii) What does each point on the graph of m represent? Give an example.e) Expand and simplify the expression to explain why the graph of m(x) isalways a straight line, regardless of the value of h.2MTE 494 04/20/10f) What does this simplified expression tell you about changes in the object's averagespeeds over
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