Contextual Applications of Differentiation

Reference:https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new

Sources: https://teachingcalculus.com/unit-4-contextual-applications-of-differentiation-2/

BC Module 4 DBA (written portion) This is a NON-CALCULATOR assignment. Show all your work to support your answers. Handwrite your work on a separate sheet of paper and upload directly to this assignment. (5 points each) For 0 s t s 6 seconds, a screen saver on a computer screen shows two circles that start as dots and expand outward. (a) At the instant that the rst circle has a radius of 9 centimeters, the radius is increasing at a rate of g centimeters per second. Find the rate at which the area of the circle is changing at that instant. Indicate units of measure. { b) The radius of the first circle is modeled by w(t) = 12 129'"5t for 0 s t s 6, where wot) is measured in centimeters and t is measured in seconds. At what time t is the radius of the circle increasing at a rate of 3 centimeters per second? (c) At what time for 0 s t s 6 is the radius of the first circle speeding up or slowing down? Justify your answer. (d) Selected values for the rate at which the radius of the second circle is changing are provided below where v is a twice differentiable function and v is measured in centimeters, t is measured in seconds and 12(0) = 3cm. we) 4 2. i 0 -l .2 -3 2 i Find . VG) 36" 3'33 2m) 6