Differentiability/ Continuity Confusion

G

Guest

Guest
Hi! I just started calculus and I'm excited but very confused. I don't understand the concept of Differentiability/Continuity. For example, these are some of the problems I was given: find every x-value at which the function is differentiable and the function is the absolute value of x+3; also how would i figure out the derivatives from the left and the right at x=1 (if they exist)and the function is equal to (x-1)^3, x is less then or equal to 0 and also the function is equal to (x-1)^2, and x is greater then 1. I really don't understand how to approach this, so please help.
 
If you think of "differentiable" as "having a well-defined slope", then where is the slope of an absolute-value function not well-defined?

Eliz.
 
Why at x = 0? What happens there? Your function is f(x) = |x + 3|, right? Is there something special at x = 0, or somewhere else?

Eliz.
 
well x=-3 is part of the answer in my book. here's the answer: (negative infinity, - 3) or (-3, infinity). I don't get where infinity comes in.
 
Basically, the function is differentiable for any x value other than -3. The negative infinity and infinity are there to cover ALL values either side of
x = -3.
 
You must log in or register to reply here.
Top