Post 4

This week we worked with first derivatives, second derivatives, differentiability, and justification. We learned about the first derivative test last week:

1. take a derivative
2. set equal to zero
3. solve for x
4. set up intervals using step 3
5. plug in first derivative
6. to find absolute value, mad/min, plug values from #5 into origional function
*remember to check for points of continuity

The second derivative test is just like the first derivative test, except you take the second derivative. When we were first learning about the second derivatives on the graphs at the beginning of last week, I didn't really follow what it was. This week I realized you're just taking the derivative of a derivative.

EX:
f(x) = 2x^3 + 4x^2 + 3x
you would take the derivative (first derivative) of this and get
f '(x) = 6x^2 + 8x + 3
after this, pretend like the derivative you just took is some origional function, and take the derivative of it, leaving you with
f "(x) = 12x + 8

This would be the second derivative. For the second derivative test, you would just take the first derivative, the second derivative, and follow the steps for the first derivative test using the second derivative.

The second derivative can help for a few things. It can be used to find points of inflection ad intervals of concavity. It is also a shortcut to find maximums and minimums. We just have to remember that points of inflection only happen if there is a change in concavity.

We also learned to justify our answers. All this basically is, is after you finish a problem, you write a paragraph on every single step you did. Also remember to include which derivative you are using and which derivative you are plugging x values into.

My question this week is differentiability in general. I missed that day and I'm looking at my notes and I'm not following. Can someone please explain?