Question 1113064
<br>
f ( x )= x^3 + ax^2 + bx + 5<br>
f'(x) = 3x^2 + 2ax + b<br>
The derivative is 0 where there are maxima or minima -- at x=-3 and x=1:<br>
{{{3(-3)^2+2a(-3)+b = 27-6a+b = 0}}}
{{{3(1)^2+2a(1)+b = 3+2a+b = 0}}}
{{{27-6a+b = 3+2a+b}}}
{{{27-6a = 3+2a}}}
{{{24 = 8a}}}
{{{a = 3}}}
{{{3+2(3)+b = 0}}}
{{{9+b = 0}}}
{{{b = -9}}}<br>
The function is f(x) = x^3 + 3x^2 - 9x + 5.  A graph:<br>
{{{graph(200,300,-6,3,-10,40,x^3 + 3x^2 - 9x + 5)}}}