Relative/Absolute Extrema homework problem

[Leprechaun]

I'm stumbling over some calc homework and was hoping someone could help me with it.

Let f be a continuous function with the following properies:

i) the domain of f is -10≤x≤10
ii) the range of f is 0<f(x)<1
iii) the dericative, f'(x), is given in the table below for selected integral values of x. Assume that for values of x between those given in the table, the derivative is between the corresponding values of f'(x) in the table.

X__|__ f'(x)
-10 | .000045
-3.0 | .045
-2.0 | .105
-1.0 | .197
0.00 | .25
1.00 | .197
2.00 | .105
3.00 | .045
10.0 | .000045


Find the x-coordinate of all relative and absolute minima and maxima of f, and of all points of inflection of f on the interval. Then, given that f(0)=0.5, sketch the graph of f.

Could someone tell me how to start off or how I should be looking at it? I don't understand how to find that information from the table.

Thanks

 

[tkhunny]

f'(x) > 0 for all x? I'm a little worried about the discrete values. This does not necessarily say much about the continuous case.

f'(x) is symmetical about the Origin? An Even function.

 

[Leprechaun]

er... I'm feeling rather clueless right now. I'm afraid I don't have the vaguest clue as to what your first statement means.

I did look up what an even function was. How does knowing that the derivative is even help me find the minima and maxima of f? Is it something obvious that I'm just not seeing?

 

[tkhunny]

If you know the value at x = 3 and at x = 2, what do you know about the value at x = 2.5? You will have to assume some continuity in order to proceed.

If f'(x) is EVEN, what dies that make f(x)? It's not necessarily and ODD function, but it IS related to one.

This particular f'(x) looks suspicious. Check this out: http://en.wikipedia.org/wiki/Logistic_curve