For this week we started on chapter two, and it is pretty easy so far. Chapter two deals with derivatives being differentiable. There are three major ways a function is not differentiable. A function is not differentiable if:
1. There is a corner (there is a corner if there is an absolute value or a piecewise)
-Also to see if there is a corner, you graph the function.
2. Vertical tangent line
-A hint for a vertical tangent line is if the exponent is x=^odd/odd
3. If it is not continuous it is either a jump, removable, vertical asymptotes
4. Lastly, if there is a cusp.
-A cusp is when x=even/odd. When graphing a function a cusp will show up as a dip in the graph.
**If a function is differentiable however, it is continuous.
*Sin x is differentiable, and sin absolute value of x has a corner.
Ex: Where is |x+2| not differentiable?
-Set what is inside equal to 0. X is differentiable at x=-2
Ex: Where is (x+3)^3/7 not differentiable?
-Notice that the exponent is x^odd/odd which makes it a vertical tangent line. The answer would be x=-3
**If it asks you to describe the x-values at which f is differentiable you would graph it, and from there remember the rules that make functions differentiable. The answers usually deal with infinity and negative infinity.
-Now for something I don’t understand. I do not understand when the function is a piecewise and from there you have to draw a graph then erase parts of it. I find that really confusing.
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