First off, i hope everyone had a great Easter break. Let's recap on some things before we get back into the swing of school.
First derivative test: You have to take the derivative of the function and set it equal to zero. Then you solve for the x values (critical points) and set them up into intervals between negative infinity and infinity. Then you plug in values between those intervals into the first derivative to find max or mins or if the graph is increasing or decreasing.
Second derivative test: You take the derivative of the function twice and set it equal to zero. You solve for the x values and set them up into intervals between negative infinity and infinity. You plug in numbers between those intervals into the second derivative to see where the graph is concave up, concave down, or where there is a point of inflection.
Tangent lines: You will be given a function and a x value. If no y value is given, plug the x value into the original function to find the y value. Then take the derivative of the function and plug in the x value to solve for the slope. Then you put everything into point-slope form (y-y1=slope(x-x1).
Limit Rules:
If the degree on the top is bigger than the degree on the bottom, the limit is infinity
If the degree on the top is smaller than the degree on the bottom, the limit is zero.
If the degree on the top is the same as the degree on the bottom, you divide the coefficients to get the limit.
Things i still do not understand:
optimization
angles of elevation
related rates
particle problems
inverse of f problems
Have a great week everyone :)
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the particle problems i can prob help you with in class..usually i have a general understanding of them :) so just remind me!
ReplyDeleteSteps for Optimazation
ReplyDelete1 Identify primary and secondary equations your primary is the one your or maximizing or minimizing and your secondary is the other equation
2. Solve for your secondary variable and plug into your primary equation if your primary only has on variable this isn�t necessary
3. Plug into secondary equation to find the other value check your end points if necessary
Steps in order to optimize anything:
ReplyDelete1. Identify primary and secondary equations. Primary deals with the variable that is being maximized or minimized. The secondary equation is usually the other equation that ties in all the information given in the problem.
2. Solve the secondary equation for one variable and then plug that variable back into the primary. If the primary equation only have one variable you can skip this step.
3. Take the derivative of the primary equation after plugging in the variable, set it equal to zero, and then solve for the variable.
4. Plug that variable back into the secondary equation in order to solve for the last missing variable. Check endpoint if necessary to find the maximum or minimum answers.
Angle of Elevation problems usually involved a triangle...and you use the tan, sin, or cos function, depending on what you have, and take a derivative to find your answer. We haven't seen one of these in a long time, so I wouldn't worry too terribly about it.
ReplyDeleteRelated rates are really really easy...like most of the time, it's almost like optimizing except you will use a lot of dVAR/dt, where VAR is like x, y, r, V, whatever your variable is.
ReplyDeleteThe hardest problem about these is just remembering your formulas...For instance, you need to remember that the volume of a sphere is 4/3(PI)r^3.