Monday, February 27, 2012MAT 121. Monday, February 27, 2012MAT 121 How calculate limits? (a) Try subbing in value! (b) Simplify if possible and return.

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Monday, February 27, 2012MAT 121

Monday, February 27, 2012MAT 121 How calculate limits? (a) Try subbing in value! (b) Simplify if possible and return to (a). (c)Use a numerical approach: Sub in values closer and closer to the limiting input value. (d)Look at a graph of the function and visualize the limit. (e) Play the S & S Game: Identify SIZE and SIGN

Monday, February 27, 2012MAT 121

Monday, February 27, 2012MAT 121

Monday, February 27, 2012MAT 121

Monday, February 27, 2012MAT 121 We have determined relative max and relative min values using first derivatives. We now focus on identifying the MOST EXTREME values among those RELATIVE possibilities. Often, this involves LIMITING THE DOMAIN, and, therefore, considering what occurs at the END POINTS. Here are examples.

Monday, February 27, 2012MAT 121 (A)For f(x) = 3x 4 + 4x 3 + 1, determine its absolute extreme values over the interval [−2,1]. (B)If g(x) = x – 2√x: (i) determine its absolute extreme values over the interval [0,9]. (ii) determine its absolute extreme values for all x. (C)For 2006, operating rate of factories, mines, and utilities in a certain region of the country, expressed as a % of full capacity, is given by the function shown below, where 0 ≤ t ≤ 250 is measured in days. On which of the first 250 days of 2006 was the rate the highest?

Monday, February 27, 2012MAT 121

Monday, February 27, 2012MAT 121

Monday, February 27, 2012MAT 121

Monday, February 27, 2012MAT 121 If exactly 200 people sign up for a charter flight, Leisure World Travel Agency charges $400/person. However, if more than 200 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Hint: Let x denote the number of passengers above 200. Determine the revenue function R(x). Determine how many passengers will result in a maximum revenue for the travel agency. What is the maximum revenue? What would be the fare per passenger in this case?

Monday, February 27, 2012MAT 121 An open-topped box is to be created from a rectangular piece of tin that measures 20 cm by 32 cm. The box is created by removing congruent squares from each corner of the rectangle and then folding up the flaps. What is the measure of the largest square that could be removed from each corner? If each cut-out square measures x cm on each side, what is a formula for the volume of the resulting box? What value of x generates the largest volume? What would be the volume in this case?

Monday, February 27, 2012MAT 121