Tangent lines:
The problem will give you a function and an x value. Sometimes they may give you a y value; if not then you plug the x value into the original function and solve for y to get the y value. Next, you take the derivative of the function and plug in x to get the slope. After that, you plug everything into point-slope form.
First derivative test:
For the first derivative test, you are solving for max and mins and may be trying to see where the graph is increasing and decreasing. You take the derivative of the function and and set it equal to zero and solve for the x values (critical points). Then you set those points up into intervals between negative infinity and infinity. Then, you plug in numbers between those intervals to see if it is positive or negative.
Second derivative test:
For the second derivative test, you are solving to see whether the graph is concave up, concave down, or where there is a point of inflection in the graph. You take the derivative of the function twice and set it equal to zero and solve for the x values. You set those values up into intervals between negative infinity and infinity. You then plug in numbers between those intervals to see if it is positive or negative. If it is positive, it is concave up. If it is negative it is concave down. Where there is a change in concavity, there is a point of inflection.
What I don't understandd:
The problems where they give you a graph and you have to seperate them into triangles and rectangles to find the area.
Integrals with trig functions in them
Theproblems where they give you two equations and you have two variables (most of the time a and b) and you have to solve for one and solve for the other and then set equal.
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ReplyDeletewell, what you need to know for the area of graphs are the area formulas:
ReplyDeletetriangles - 1/2*b*h
rectangles - l*w
seperate the graph...and then add them up
usually the problems like this are asking for total distance
HOPE THIS HELPS!
Most of the time, the graph is of velocity or position. You have to separate the graph into different shapes such as triangles and rectangles. You then solve each of the area formulas for each shape and add the areas together. Hope this helps!
ReplyDeleteYou need to find out the shapes among the graphs. take the area of each shape using the formulas and add them together.
ReplyDeleteFor the trig integrals, just remember the formulas (including all of the strange ones from Advanced Math) and work backwards =]
ReplyDelete