Rate of Change of a Function

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Questions

• What is Rate of Change of a Function?
• How do you determine the rate of change of a function?
• What are partial derivatives?
• How do you find a function f(x), which, when multiplied by its derivative, gives you #x^3#, and for which #f(0) = 4#?
• How do you graph the derivative of a function when you are given the graph of the function?
• What is the purpose of a derivative?
• How do you solve the AP Calculus 2013 Free Response question #3? http://media.collegeboard.com/digitalServices/pdf/ap/apcentral/ap13_frq_calculus_ab.pdf
• A factory produces bicycles at a rate of 80+0.5t^2-0.7t bicycles per week (t in weeks). How many bicycles were produced from day 15 to 28?
• The cost function for a product is C(x)=0.8x^2 +120x+110. How to find average cost over [0,600] ?
• A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2ft/s, how fast is the angle between the top of the ladder and the wall changing when the angle is #pi/4# rad?
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• Question #fdebb
• Question #a364e
• A rectangle's base remains 0.5 cm while its height changes at a rate of 1.5 cm/min. At what rate is the area changing, in cm when the height is 1.5 cm?
• Suppose the population of a town grows according to the equation #y=100t+t^2#, how do you find the rate of growth at time t=100 years?
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• Question #9a735
• The volume of a sphere is changing at a constant rate of #pi/3 \ cm^3s^-1#. How fats is the surface area changing when the volume is #(9pi)/2#?
• Can someone help out with the question below?
• If #P=215-5Q#, what is price elasticity of demand when #P=15#. (1) #43#; (2) #40#; (3) #-5#; (4) #-0.075#?
• A ladder is leaning against a wall, and the floor and slipping. If the bottom of the ladder is slipping at #30 cms^(-1)# then how fast is the top of the ladder sliding down the wall when the ladder is at #45^o#?
• Question #16171
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• Question #f1456
• Suppose you are blowing a spherical bubble, filling it in with air at a uniform rate of 400mm^3/s. How fast is the radius of the bubble increasing by the time it is already 20mm long?
• The temperature T in #""^oC# of a particular city during a 24 hour period can be modelled by #T = 10 + 8 sin 12 pi t# where t is the time in hours, with t = 0 corresponding to midday. Find the rate at which the temperature is changing at 4pm.?