# Sketch the graph problem

1. Mar 29, 2007

### afcwestwarrior

sketch the graph of a function that has no local minimum at 2 and is differentiable at 2

this is confusing, how come this is an upside down parabola, it makes sense, but how do i know what kind of graph to draw

2. Mar 29, 2007

### Staff: Mentor

There must be more to the question. Infinitely many functions have no local minima at 2 and are differentiable there. What else is given in the problem or in the discussion that precedes the problem?

3. Mar 29, 2007

### afcwestwarrior

mmm, no what i wrote it wrong i meant local maximum, my bad.

4. Mar 29, 2007

### Staff: Mentor

Well, maybe when they said sketch the graph of *a* function, they meant any of the infinitely many functions that obey the criteria. Woudn't a horizontal line work?

5. Mar 30, 2007

### HallsofIvy

Staff Emeritus
Again, are you sure you have written the problem correctly? Almost any graph except the upside down parabola you mention would work. Are you sure the problem did not say "has a local maximum at x=2" rather than "has no local maximum"?

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