This week in Calculus we did optimization and reviewed. So, that’s what I’m going to do..explain things I now understand from the beginning of the year, and say I still don’t understand how you know what is the primary and secondary functions for optimization.
So, FIRST DERIVATIVE TEST: let c be a critical point of a function, f, that is continuous on an open interval containing c. If it is differentiable on the interval, except possibly at c, then f[c] can be classified as either:relative min [negative to positive]relative max [positive to negative]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
SECOND DERIVATIVE TEST: concavity & points of refection. 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.
Also, I understand the LIMIT RULES…Remember, you find vertical asymptotes when you set the bottom of a fraction equal to zero, then solve. After you factor the top and bottom of the fraction, if there is anything you can cancel from a function, it is a removable. Another thing i understand better is how to use the first and second derivative test.
I need help with tangent lines and optimization when figuring out which formula is what…can anyone help?
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