Calculus Section 3.9 Solve applications of implicit differentiation. A function can be differentiated with respect to a variable that does not appear within.

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Presentation transcript:

Calculus Section 3.9 Solve applications of implicit differentiation. A function can be differentiated with respect to a variable that does not appear within the function if implicit differentiation is used. Find the derivative of the function with respect to t. x 3 + 5x 2 – 2y = 19 (Find )

example A Japanese beetle infestation is spreading from the center of a small town. The beetles fly off in all directions, so the region they cover is circular. The radius of the circular region is increasing at a rate of 1.5 miles per year. Determine the rate of change of the area of infestation when the radius is 4 miles.

example A manufacturer of tennis balls decides to increase the production at a rate of 30 packages per day. Total revenue from the sales of all x packages produced is R=2.14x-.0001x 2 dollars. Determine the rate of change of revenue with respect to time when the daily production level is 1500 packages.

example A kite is flying 150 ft high, where the wind causes it to move horizontally at a rate of 5 ft per second. In order to maintain the kite at a height of 150 feet, the person must allow more string to be let out. At what rate is the string being let out when the length of the string already out is 250 ft?

assignment Page 171 Problems 2-24 even