If f is continuous function for all x ∈ R and f(f(x))=1+x, then find value of f'(1).
The function I chose in this graph is not differentiable at 1. It's piecewise with f and g together forming a single function.
https://www.desmos.com/calculator/xgpuepws65
I could shift the function up or down the line y=x+1/2 to make the derivative either 3 or 1/3. I could also change the degree of shift to make the derivative any positive number.
Note my graph looks like sawtooth graph rotated 45 degrees. I think Charlie's idea would have worked has he rotated a sine wave instead of adding x.
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Posted by Jer
on 2025-05-07 11:13:42 |
It's not unique
