Question

Can someone show me step by step how this problem is done?

Answer 1

i have an idea and notes but would like this problem clarified

Answer 2

i know for sure its not differentiable at corners

Answer 3

Well, all of those functions are continuous and differentiable by themselves, so your only candidates for non-differentiable points are at the places these functions overlap, or in this case, 2 and 7. However, we find that \[\lim_{x \rightarrow 7^-} f(x) = 2 - (7) = -5\] , but \[\lim_{x \rightarrow 7^+} f(x) = 7^2 + 6 = 55\] , so the function is not continuous at x=7, eliminating that option. Our only other option is x = 2, and the function approaches the same value (0) from each side, so it is continuous. In addition, because the derivatives of the functions (x-2) and (2-x) are different for all x, it follows that the slope from the left and the slope from the right at x = 2 are different, making the function non-differentiable at x=2, so the only point where the function is both continuous and non-differentiable is at x=2. Hope I explained that clearly enough!

Answer 4

could you show me what you said using numbers and graphs rather than words. im more of a visual person when it comes to math.

Answer 5

Sure thing, one second.

Answer 6

ok, sweet. sorry if im being a pain.