Lecture 9 Flashcards
how do you interpret the practical meaning of a function?
read the entire scenario and gain meaningful insight not only in terms of the variables. Also, try and visualize the scenario
how do you state the units of a derivative?
the units of the y value over the units of the x value
how do you interpret the meaning of an inverse function?
the meaning of the y value now becomes the x value and the meaning of the x value now becomes the y value
how do you interpret the meaning of an inverse derivative function?
the meaning of the y value now becomes the x value and the meaning of the x value now becomes the y value. Now interpret this in terms of the rate of increase or decrease
what is the difference between the graph of the first and second derivative?
the second derivative graph will have less turns
what does concave up mean in terms of slopes?
the slope changes from negative to positive
what does concave down mean in terms of slopes?
the slope line changes from positive to negative
what does it mean if the second derivative is positive in terms of concavity?
concave up
what does it mean if the second derivative is negative in terms of concavity?
concave down
what is the rate of growth of a concave-up function doing?
increasing
what is the rate of growth of a concave-down function?
decreasing
which function illuminates the nature of a yearly cycle?
a periodic functions like sine or cosine
what is a tip to find the limit of a composite function?
work from the inside out
