AB Review Day 3
1) List the derivative and integral formulas for the natural log and exponential functions.
2) List the trig derivatives for all six trig functions.
3) List the trig integrals for all six trig functions.
4) Find the inverse of the following function: f(x) =
x3  3
.
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5) Describe the process of how to find the derivative of an inverse function.
6) List the derivatives and integral formulas for exponential functions whose bases are not e.
7) Create and solve a problem that finds the derivative of an exponential function with base other than e.
8) Solve: A bacterial culture grows in such a way that it models exponential growth. The culture has an initial population
of 50 and doubles in size every 3 hours. Determine the equation for finding the bacterial culture’s population at any
time, t. Then, determine how long it will take for the culture to be 1000 times its starting size.
9) List the formulas for inverse trig derivatives and integrals.
10) Create and solve a problem that involves inverse trig integration.
11) Describe the process for filling out a slope field and drawing a solution curve.
12) Solve the differential equation: xy + y’ = 100x
13) Write the basic equation for logistic growth and draw the solution curve. Label all the points of interest,
increasing/decreasing, and concavity of the graph.