Open Middle®
Directions: Using the digits -9 to 9, at most two times each, place a digit in each box so that the function is nondifferentiable at the given x value.
Extension: Can you make the function continuous but nondifferentiable?
Hint
What things can make a function nondifferentiable?
Answer
There are many answers across the multiple types of nondifferentiability. Some examples are:
1. |4x+8|/|x-2| is nondifferentiable at -2 because of a sharp turn and at 2 because of a vertical asymptote.
2. |2x + -6|/|x-3| is nondifferentiable at 3 because it is undefined at that point.
1. |4x+8|/|x-2| is nondifferentiable at -2 because of a sharp turn and at 2 because of a vertical asymptote.
2. |2x + -6|/|x-3| is nondifferentiable at 3 because it is undefined at that point.
If you are using the extension, then the only type of nondifferentiability allowed is a sharp turn.
Source: Owen Kaplinsky
answer is -pi s squared
The extension about making it continuous but nondifferentiable is the real brain-bender—it forces you to think about limits matching up while slopes don’t. I tried a piecewise approach with absolute value disguised under digits, but keeping the sharp turn within those digit constraints took a few tries.