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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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i have an idea and notes but would like this problem clarified
i know for sure its not differentiable at corners

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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!
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.
Sure thing, one second.
ok, sweet. sorry if im being a pain.
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Sorry I'm not a better artist, but basically, at x = 2, the function approaches the same value from the left and right, but at different rates, so it is continuous, but not differentiable. At x = 7, there is a massive jump in the graph, so it is not continuous nor differentiable
how did you put the info given in your calculator to get this graph
?

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