1. Take the derivative like you would when taking a regular derivative. All the same rules apply.
2. Everytime you take the derivative of y you label it dy/dx or y'.
3. Lastly, you solve of dy/dx or y' depending on what you noted it as.
EXAMPLE:
4y^3 + 2y^2 + 6y - x^2 = 5
Derivative: 12y^2 dy/dx + 4y dy/dx+ 6 dy/dx - 2x = 0
Add the 2x to have all dy/dx on one side
12y^2 dy/dx + 4y dy/dx + 6 dy/dx = 2x
Factor out a dy/dx
dy/dx ( 12y^2 + 4y + 6) = 2x
Finally you divide 2x by 12^2 + 4y + 6 to get your answer
2x/ 12y^2 + 4y +6
If you are trying to find the slope of a tangent line, it is the same steps as finding it with a regular derivative, except you use the implicit derivative steps to find the derivative. You still, however, have to find a y-value by plugging in for x, take the derivative and set it equal to zero, and instead of solving for x, you solve of dy/dx and then plug in your x and y values and simplify if needed.
For what I'm still having trouble with is looking at graphs of f'(x) and determining where the f''(x) is concave up or down or where f(x) is increasing or decreasing, such as the questions on the short answer part of the. How to find points of inflection given f'(x) also confuses me sometimes.
I'm going attempt to do my homework now.
When looking at the graph you really just need to sit down with yourself mentally and sort out what they need and how different functions relate to each other.
ReplyDeleteSo really, things you need to remember:
first derivative = the zeros of this function (where it crosses the x-axis) will always be the maxs or mins of the original function. if the first derivative is above the axis (positive) then the original is increasing. if it is below, it's decreasing.
second derivative = the zeros of this function are the the max's or min's of the first derivative. (and vice versa, remember that). where this is positive, the original is concave up. where it is negative, the original is concave down.
identifying different areas of a graph are all about getting the terminology right. theres no calculus involved at all. it's just a matter of getting used to the wording.
hope this helps a bit :-)
Graph example: http://s180.photobucket.com/albums/x15/ryanb985/?action=view¤t=scan0001.jpg
ReplyDelete