This week in calculus we started off working some more optimization problems and then took a quiz on optimization. I understood the concept of optimization and how to work it, i just need help figuring out my different formulas.
After the quiz, we started working on exam study guides in class. I understand the derivative packet the best. I also understand what to do when they ask you for the slope of a function and when they ask for an equation to the tangent line.
For those of you who are still struggling with derivatives, heres an example of one:
8xsinx+5cosx.
the derivative of that would be
8x(cos(x)) + 8sin(x)-5sinx
to simplify that you would come out with:
8xcos(x)+5sin(x)
I also now understand how to figure out different types of limits. You find vertical asymptotes when you set the bottom of a fraction equal to zero and solve. For horizontal asymptotes, you use the three rules when looking at the degree on the top of the fraction and on the bottom. Anything you can cancel from a function is a removable. Another thing i understand better is how to use the first and second derivative test. When using the first derivative test, you take the derivative of the function and set it equal to zero and solve for x. Then you set up your x values into intervals to see which ones are max and mins etc. When using the second derivative test, you take the derivative of a function two times and set equal to zero and solve for x. You put these x values into intervals as well to find if a graph is concave up or down, point of inflection, etc.
The problems i still seem to have is how to figure out what formulas need to be used in optimization problems. After i figure that out, i can finish the problems. Another thing that i am still confused with is when they give you a graph of an original function. Then they want you to calculate what the max and min of the graph. i do not understand how to look at the original function and figure out what the first derivative is supposed to look like. If anyone can help me with these things, it would be big help.. Thanks :)
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when looking at the original graph you can find the first derivative by looking at your maxs and mins. put them on the x axis and when you see that it's increasing [from the original] you'll know that it has to go up which means that it will start down. i hope that helps...and hopefully that's right..i'm pretty sure it is though.
ReplyDelete[THE MAX AND MINS OF THE ORIGINAL ARE ALL WHERE f(x) IS EQUAL TO ZERO]