Question

Session 9 problem set. What does it mean for a function to be differentiable? and how do I find that out?

Answer 1

A function is differentiable if its slope coming from the left is the same to that coming from the right.

If you were about finding these slopes, you probably would try to find: \[\frac{\Delta y}{\Delta x}\]from the left and from the right. But considering that you are trying too find the slopes for a Δx that approaches zero, then the function is differentiable if the derivative coming from the left is equal to the derivative coming from the right at a specific point.

Answer 2

@Dalta

Answer 3

The idea is that the two "branches" of the curve must meet at the same point for the curve to be differentiable everywhere. In other words, you want a "continuous" function (over the domain of interest), and continuous means "no jumps"
See attached examples

Answer 4

To answer the question, you must solve for what values of a and b make the two equations equal when x=0 (for the first problem) or when x=1 (for the second problem)

Answer 5

Thank you both, I think I get it now.