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• When more than one one function function is involved in in a a a a a problem refer to each one one by name or or symbol not as “the function” • A A function can can increase or decrease A A graph cannot Be sure to use the proper reference • When dealing with rates of of change change be precise in in in language If a a a a a a a a a a a function’s rate rate rate rate of of of of change change is is is is for example -4 -4 m/s m/s m/s either “the “the function function function is is is is decreasing at at at at at at a a a a a a a a a a a a a a a rate rate rate rate of of of o of 4 4 4 4 m/s” m/s” or or or “the “the “the function function function is is is is changing at at at at at at at a a a a a a a a a a a a a a a rate rate rate rate of of of o of -4 -4 -4 m/s” m/s” Students often write (incorrectly) “the “the function function is is decreasing at at at at at a a a a a a a a a a rate rate rate of of o of -4 -4 m/s m/s m/s ” ” ” • If a a a a a a a function’s derivative derivative is is is positive the the function function is is is increasing increasing Too often students write “the derivative derivative is is is is increasing” and while that might be be true it it is is not the the answer being sought • When interpreting a a a a a a a a a a result in tin in in in context always include numerical value units and time as appropriate For example “The vehicle is moving to the right at at at 60 mph at at at 3:15 pm "
HOW SULLIVAN AND AND MIRANDA’S CALCULUS FOR THE AP® COURSE 3E CAN HELP:
• Sullivan and and and Miranda break down their worked examples step step by step step to demonstrate precise mathematical language and and and and style for students In addition they provide clear definitions theorems and and other explanations throughout the the text • CALC CLIPS for students are helpful videos where an an expert teacher works through a a a a a a a a a a a a a worked example or or or or or practice problem and visually demonstrates how to notate the the correct mathematical style