Graphing a Function with No Local Minimum at x=2 and Differentiable at x=2

[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

 

[berkeman]

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?

 

[afcwestwarrior]

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

 

[berkeman]

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?

 

[HallsofIvy]

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"?