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anonymous
 4 years ago
Can someone show me step by step how this problem is done?
anonymous
 4 years ago
Can someone show me step by step how this problem is done?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i have an idea and notes but would like this problem clarified

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i know for sure its not differentiable at corners

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Well, all of those functions are continuous and differentiable by themselves, so your only candidates for nondifferentiable 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 (x2) and (2x) 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 nondifferentiable at x=2, so the only point where the function is both continuous and nondifferentiable is at x=2. Hope I explained that clearly enough!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0could you show me what you said using numbers and graphs rather than words. im more of a visual person when it comes to math.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Sure thing, one second.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok, sweet. sorry if im being a pain.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1328394320991:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Sorry 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0how did you put the info given in your calculator to get this graph
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