<PRE><B>Question 1163320</B>
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A local maximum or minimum means the slope of the graph is 0; that means the derivative of the function is 0.&lt;br&gt;
The given function is a 3rd degree polynomial; its derivative will be a 2nd degree polynomial.  That is consistent with the given information that the function has one local minimum and one local maximum.&lt;br&gt;
Find the derivative of the function:&lt;br&gt;
{{{df/dx = 3ax^2+12x+b}}}&lt;br&gt;
Use the fact that the derivative is 0 at x=-1 and x=2 to form two equations in the unknowns a and b.&lt;br&gt;
{{{3a(-1)^2+12(-1)+b = 0}}}
{{{3a-12+b = 0}}}
(1) {{{3a+b = 12}}}&lt;br&gt;
{{{3a(2)^2+12(2)+b = 0}}}
{{{12a+24+b=0}}}
(2) {{{12a+b = -24}}}&lt;br&gt;
Subtracting (1) from (2)...&lt;br&gt;
{{{9a = -36}}}
{{{a = -4}}}&lt;br&gt;
Then substituting a=-4 in either (1) or (2) gives b=24.&lt;br&gt;
ANSWER: a = -4; b = 24&lt;br&gt;
A graph...:&lt;br&gt;
{{{graph(400,400,-4,4,-20,60,-4x^3+6x^2+24x+4)}}}&lt;br&gt;
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For tutor @ikleyn.....&lt;br&gt;
My goodness! Grow up!&lt;br&gt;
Do you feel slighted because I felt a solution identical to yours but presented differently might be useful to the student?!&lt;br&gt;
Your solutions are NOT always the solutions that are the best possible for the particular student.  The same solution presented differently might satisfy the student&#39;s needs better....&lt;br&gt;
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