Help
Options
Didn't know it?
click below
click below
Knew it?
click below
click below
Don't Know
Remaining cards (0)
Know
retry
shuffle
restart
0:00
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
Calc Ch. 7 and 8.2
Dr. Shelly, AP Calculus BC Chapter 7 and 8.2
| Question | Answer |
|---|---|
| Euler's Method for Solving Differential Equations | 1. Solve the differential equation for dy in terms of x, y, and dx, 2. Substitute values of x, y, and dx to calculate a value of dy, 3. Find the approximate new value of y by adding dy to the old value of y, 4. Repeat procedure to find next dy at next x |
| Logistic Differential Equation | dy/dx=ky*(M-y)/M or dy/dx = k/M*(y)(y-M) where M is the maximum sustainable value of y as x increases & k is a proportionality constant |
| Logistic function | y = M/(1+ae^(-kx)), the solution of the logistic differential equation, where the constant a is determined by the initial condition |
| critical point | occurs at x = c if and only if f(c) is defined and f '(c) is either zero or is undefined |
| point of inflection or inflection point | The point (c, f(c)) if and only if f "(x) changes sign at x = c |
| cusp | (c, f(c)) if and only if f ' is discontinuous at x =c |
| plateau point | (c, f(c)) if and only if f '(c)=0, but f '(x) does not change sign at x = c |
| local maximum | If f ' (x) goes from positive to negative at x = c, and f is continuous at x = c |
| local minimum | If f '(x) goes from negative to positive at x = c, and f is continuous at x = c |
| concave up at x = c | If f "(c) is positive |
| Concave down at x = c | If f "(c) is negative |
| The second derivative test | If f '(c)=) and f "(c) is positive, then f(c) is a local minimum. If f '(c)=0 and f "(c) is negative, then f(c) is a local maximum. If f '(c) & f "(c)=0, then it is not distinguishable |
Created by:
sissiloo
Popular Math sets