<PRE><B>Question 1138898</B>
&lt;br&gt;
(1) f(x) is odd.&lt;br&gt;
That means the graph is symmetric with respect to the origin.
That in turn means that f(0) = 0.&lt;br&gt;
(2) f&#39;&#39;(x) is positive for all x &gt; 0.&lt;br&gt;
That means the graph is concave up for all x &gt; 0.
The fact that f(x) is odd then means the graph is concave down for all x &lt; 0.&lt;br&gt;
(3) f&#39;(0) is negative.&lt;br&gt;
That means the slope of the graph at x=0 is negative (downhill to the right).&lt;br&gt;
(4) f&#39;(1) = 0.&lt;br&gt;
That means the slope of the graph is 0 (the tangent to the graph is horizontal) at x=1.
That in turn means the slope is also 0 at x = -1.&lt;br&gt;
(5) f(2) = 0.&lt;br&gt;
That means that f(-2) = 0 also.&lt;br&gt;
I can&#39;t draw a graph of such a function, because no kind of graph that I know how to graph with the tools on this forum has all those characteristics.&lt;br&gt;
The graph below of the polynomial {{{y = x^3-4x =(x+2)(x)(x-2)}}} almost works, except that the slopes of 0 are not at exactly x=1 and x=-1.&lt;br&gt;
{{{graph(400,400,-3,3,-10,10,x^3-4x)}}}</PRE>