This past week in calculus we reviewed for our mid- term exam. Mrs. Robinson explained to us the concepts of finding max and mins when looking at a graph. When looking for max and mins, put a filled in circle where the graphs change from increasing to decreasing, for points of inflection, put open circles where the graphs change concavity.
Another thing we reviewed was the equation of a tangent line. When you are given a function and an x point. You take the derivative of the function and plug in the x value to find the slope. To find the y value, plug the x value into the original function and solve.
Another thing was solving for dy/dx. All you do for these is taking the derivative like normal but everytime you take the derivative of a y, you put dy/dx behind it. After the derivative has been taken, you solve for dy/dx.
One thing i have become very good at is finding the relative extrema of a function. If they give you points, you plug the points into the original function. You will get another number and you put the numbers together like points. Then to find more points, you take the derivative of the function and solve for x to find the critical points. You plug the critical points in to the original function and get another point. When everything has been plugged in, you figure out which point is the highest and which one is the lowest. Those points will be your relative max and relative min.
To find out if the function is increasing or decreasing, you take the derivative of the original function and solve for x to find the critical values. Then you plug those points into intervals. You take a number between each interval and plug that number into the derivative, if the number is positve it is increasing, if the number is negative it is decreasing. This is the way you find regular max and mins as well.
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