This week we did many new things. We started off everyday with a derivative problem on the board. I think this is good, because I need practice simplifying. We learned about differentiability. We also learned how to justify something. We also learned more about first and second derivatives.
Something I understood this week was taking first derivatives.
Let's say you need to find the critical values of (x^3 - 1)/x.
You would first take the derivative of this and get (2x^3 + 1)/(x^2).
You would then the derivative equal to zero to find you critical values.
You're critical values are x = (-1/2)^1/3.
Something I did not understand was what Differentiability is. I don't get what it means to have a differentiabily.
I don't really get the second derivative test either, with all the concave up, concave down nonsense.
Ryan
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differentiability is where the points of discontinuity is..
ReplyDeletei can't really help you with the second derivative thing..
all i know are the steps.
derivative, derivative, set = 0, intervals, plug in..
The second derivative test is very similar to the first derivative test. Instead of taking the derivative and then setting it equal to zero, you take the derivative of the derivative and then set equal to zero. Then you have your intervals, which you plug in just like you would for the first derivative. The only difference is if it is positive then it is concave up, but if it is negative it is concave down. At the point were concavity changes is where your point of inflection is.
ReplyDeletewhen you get your intervals a positive one is concave up and a negative one is concave down
ReplyDeleteThe second derivative test is just like the first derivative test, except at the beginning, you go one step further and take the derivative of the first derivative, which is the second derivative. When you get your possible points of inflection and set up intervals, they tell you at which points your graph is positive or negative. Just think of it as a max and a min. If a graph would have a min at the point, the hump concaves up (like a bowl), and if it would have a max at the point the hump would concave down (like an umbrella)
ReplyDeletei don't know much about differentiability but i know that for the second derivative, all you have to do is take the derivative of the first derivative, then you set the top equal to zero, factor, from that you get your possible points of inflection, then from that you set up intervals to find the concavities and to find your points of inflection.
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