 In this video we present the solution to question number three for practice exam number two for math 1210 in which case we are given a function by its graph illustrated here determine all the values of x for which f is not differentiable. So remember there's three things we need to look for for a function to not be differentiable. So the first thing we have to look for is going to be discontinuities. If there's any discontinuities on the graph that'll make the function not be continuous. Well it won't be continuous obviously but it won't be differentiable there as well. We also are going to be looking for sharp corners. Notice our graph to the right it doesn't have any discontinuities but there are a couple corners right places where the direction suddenly changes. So we see there's a sharp corner here at x equals three. There's a sharp corner here at x equals two and there also appears to be a corner here at zero. It's not as sharp as the others but there is a sudden change in direction. The point is if we take the derivative from the left and from the right that is we look at the slope of the tangent lines. Those would disagree with each other and it would put a jump discontinuity on the derivative function. The derivative is not going to be defined there. But the other thing we have to look out for are vertical tangent lines. If there's any places where the graph has a vertical tangent then that would correspond to a vertical asymptote on the derivative function. It would be undefined at that location. So we can see at negative two there's going to be a vertical tangent. And also there's going to be a vertical tangent at negative six given the behavior of the graph right there. When it comes to the boundary there's actually no problem at x equals six right here. There's a horizontal tangent not a big deal. Horizontal tangent lines are perfectly fine. The vertical tangents we need to throw out, sharp corners we need to throw out and also any discontinuities. This question about determining where the graph is differentiable at certain points or continuous at different points is related because if the function's not continuous at a point then it won't be differentiable. But if you have a sharp corner like here it is continuous at this point but not differentiable. Also vertical tangent lines, the function is continuous at this point but it doesn't have the derivative at that point. So the numbers we need to throw out are negative six, negative two, zero, two and three which leads to the correct response being E.