<PRE><B>Question 1057331</B>
.
f(x) = 2x^3 - 4x^2 +3x - 5
for which x values is the graph concave down?
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&lt;/pre&gt;
The first derivative of f(x) is f&#39;(x) = {{{6x^2 - 8x + 3}}}.


The second derivative of f(x) is f&#39;&#39;(x) = 12x-8.


The graph is concave down  &amp;nbsp;&lt;-----&gt;&amp;nbsp;  &amp;nbsp;f&#39;&#39;(x) &lt; 0,  &amp;nbsp;&amp;nbsp;i.e.


12x - 8 &lt; 0  &lt;---&gt;  x &lt; {{{8/12}}} = {{{2/3}}}.
&lt;/pre&gt;

{{{graph( 330, 330, -3.5, 3.5, -10.5, 6.5,
          2x^3 - 4x^2 +3x - 5
)}}}


Plot y = {{{2x^3 - 4x^2 +3x - 5}}}


</PRE>