Answer:
see attached
Explanation:
You want the graph of a function with these limits and f'(3) = 0.
- as x → 4, f(x) = 6
- as x → 1+, f(x) = 2
- as x → 1-, f(x) = -2
- as x → -2, DNE
Limits
For a limit to exist, the function must approach the same value from left or right. The function need not be defined at the limit point (may have a hole), but it needs to be continuous on either side of the limit point.
If a limit does not exist, the function will approach a different value from the left than from the right. Here, the function specification of two different limits at x = 1 means the limit does not exist (DNE) there, as well as at x = -2.
Function
The attachment shows a function with f(4) = 6 on a continuous curve, f'(3) = 0, and different left/right limits at x = 1 and x = -2.
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Additional comment
Of course, there is an infinite variety of functions that will satisfy the requirements here.
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