Question 1209605
<pre>
The graph of

{{{q(x) = x^4 + 8x^2 + 7x^3}}}

{{{graph(400,400,-10,10,-100,100, x^4+8x^2+7x^3)}}}

We need to find the lowest point on the graph.

We use the derivative:

{{{"q'(x)"=4x^3+16x+21x^2}}}

and set it equal to 0:

{{{4x^3+21x^2+16=0}}}

{{{x(4x^2+21x+16)=0}}}

{{{x=0}}}; {{{4x^2+21x+16=0}}}

Solve that by the quadratic formula:

{{{x = (-21 +- sqrt(185))/8}}}

We want the lowest value which is the leftmost minimum point, so we use
the - sign

We substitute {{{x = (-21 - sqrt(185))/8}}} in

{{{q(x) = x^4 + 8x^2 + 7x^3}}}  and after much work, we get

{{{(-16571 - 1295sqrt(185))/125}}} so the range is

{{{matrix(1,5,

"[", (-16571 - 1295sqrt(185))/125,",",infinity,")")}}}

Edwin</pre>