<p> Mean Value Theorem, The Sequel</p><p>Mr. Gunther Calculus BC Name: ______Date: ______</p><p>The key concept – a flow rate can also be a function. (For example, , a velocity function, is a “flow rate” for a related position function.) So the original MVT relationship… (I) A______rate of  over an in______l = I______rate of  at a po___t can also be described as… (II) A_____ value of a f_____n over an in______l = I______value of a f_____n at a po__t</p><p>The average value of a function is given by: </p><p>So (II) above can be rewritten as </p><p>As with the original version of the MVT, this will be guaranteed to work when is d______e.</p><p>For each function and interval given below, (a) find the antiderivative of the function, (b) use the antiderivative to compute the average value of the function on the given interval, (c) apply the MVT Version 2 to find at what x-value the “point value” of the function equals the average value you computed in (b).</p><p>1) on </p><p>2) on </p><p>3) on </p><p>4) A snow squall passes and leads to snow falling at an instantaneous rate of centimeters per hour over a three-hour time frame. a. What is the average rate of snowfall per hour? b. What does the MVT say this average rate of snowfall must equal? c. Where must the t-value that the above equality occurs be located, according to the MVT? d. Find the time when the MVT is satisfied for this scenario.</p><p>5) An alternating current circuit has current flowing measured by amperes. a. What is the average rate of current flow on the interval ? b. What does the MVT say this average rate of current must equal? c. Where must the t-value that the above equality occurs be located, according to the MVT? d. Find the time when the MVT is satisfied for this scenario.</p>