Chat with AIExam 3: Differentiation
Exam 1: Preparation for Calculus125 Questions
Exam 2: Limits and Their Properties85 Questions
Exam 3: Differentiation193 Questions
Exam 4: Applications of Differentiation154 Questions
Exam 5: Integration184 Questions
Exam 6: Differential Equations93 Questions
Exam 7: Applications of Integration119 Questions
Exam 8: Integration Techniques and Improper Integrals130 Questions
Exam 9: Infinite Series181 Questions
Exam 10: Conics, Parametric Equations, and Polar Coordinates114 Questions
Exam 11: Vectors and the Geometry of Space130 Questions
Exam 12: Vector-Valued Functions85 Questions
Exam 13: Functions of Several Variables173 Questions
Exam 14: Multiple Integration143 Questions
Exam 15: Vector Anal142 Questions
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If the annual rate of inflation averages 
over the next 10 years, the approximate cost C of goods or services during any year in that decade is 
where t is the time in years and P is the present cost. The price of an oil change for your car is presently 
. Find the rate of change of C with respect to t when 
. Round your answer to three decimal places.
over the next 10 years, the approximate cost C of goods or services during any year in that decade is where t is the time in years and P is the present cost. The price of an oil change for your car is presently . Find the rate of change of C with respect to t when . Round your answer to three decimal places. (Multiple Choice)
4.8/5 
(32)
(32) Evaluate 
for the equation 
at the given point 
. Round your answer to two decimal places, if necessary.
for the equation at the given point . Round your answer to two decimal places, if necessary. (Multiple Choice)
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(47) All edges of a cube are expanding at a rate of 7 centimeters per second. How fast is the volume changing when each edge is 2 centimeters?
(Multiple Choice)
4.9/5 (34)
(34) 
. 
. Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. 
(Multiple Choice)
4.8/5 (35)
(35) Evaluate 
for the equation 
at the given point 
. Round your answer to two decimal places.
for the equation at the given point . Round your answer to two decimal places. (Multiple Choice)
4.8/5 (37)
(37) The radius of a right circular cylinder is 
and its height is 
, where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time.
and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time. (Multiple Choice)
4.8/5 (32)
(32) 
. 
.
. Find an equation of the tangent line to the graph of 
at the point 
.
at the point . (Multiple Choice)
4.7/5 (34)
(34) 
Find the points at which the graph of the equation has a vertical or horizontal tangent line. 
(Multiple Choice)
4.9/5 (33)
(33) A conical tank (with vertex down) is 12 feet across the top and 18 feet deep. If water is flowing into the tank at a rate of 18 cubic feet per minute, find the rate of change of the depth of the water when the water is 10 feet deep.
(Multiple Choice)
4.9/5 (35)
(35) The graph of the function f is given below. Select the graph of 
. 
. (Multiple Choice)
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(38) Complete two iterations of Newton's Method for the function 
using the initial guess 
. Round all numerical values in your answer to four decimal places.
using the initial guess . Round all numerical values in your answer to four decimal places. (Multiple Choice)
4.9/5 (43)
(43) Find an equation of the tangent line to the graph of the function 
at the point 
. The coefficients below are given to two decimal places.
at the point . The coefficients below are given to two decimal places. (Multiple Choice)
4.8/5 (36)
(36) Use implicit differentiation to find an equation of the tangent line to the ellipse 
at 
.
at . (Multiple Choice)
4.8/5 (40)
(40) 
at the point 
for the equation 
. 
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