Happy Holidays to everyone and i hope everyone had a great Christmas. Let's start off by reviewing first derivative test.
You take the derivative of the function and then you solve for x. Your x values will be considered your critical values. You then set these values into intervals between infinity and negative infinity. You then plug in numbers into the derivative to see if the function is increasing or decreasing on that interval. If the number is positive it is increasing, if the number is negative it is decreasing. These numbers are also considered max's and min's. To find the absolute max and mins, you take the point given to you and plug it into the orginal function to create another point. Then you take the derivative and find your critical values and plug those in as well. Whichever point is the biggest is your absolute max and whichever point is the lowest is your absolute min.
For the second derivative test, you take the derivative of the original function and take the derivative again. You solve for your critical values again like in the first derivative test, and you set them up into intervals again. This time when plugging in numbers between the intervals, if the number is positive it is concave up, if the number is negative it is concave down. There is a point of inflection wherever there is a change in concavity in the function.
Lets also go over the rules of related rates:
First define all of the given in the problem.
Second, figure out which formula they are asking you to use
Plug in all of your given.
Take the derivative and solve for the unknown.
I hope everyone has a Happy New Year!!
Bye for now :)
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