Graphing the function.

Oct 2009
Sketch the graph of a function that satisfies all of the given conditions:
f'(1)=f'(-1)=0,f'(x)<0 if |x|<1
f'(x)>0 if 1<|x|<2, f'(x)= -1 if |x|>2,
f''(x)<0 if -2<x<0, inflection point (0,1)

any help pls..


MHF Helper
Apr 2005
Where, exactly are you having a problem? First, do you understand that there are an infinite number of correct answers? You are only asked to find one.

f'(x)< 1 for |x|< 1 tells you that, between -1 and 1 at least, the function is decreasing. At -1 and 1, f'(-1)= f'(1)= 0 so the function levels off and has horizontal tangent line. f'(x)> 1 for 1< x< 2 so the function is increasing there and f'(x)= -1 for all x> 2 so the graph is a straight line downward at a 45 degree angle after x= 2. f"(x)< 0 for -2< x< 1 so the graph is "convex downward" there. Finally, there is an inflection point at (0, 1) so the graph goes through the point (0, 1) and changes convexity there.