SOLUTION: The domain of the function q(x) = x^4 + 8x^2 + 7x^3 is (-infty,infty). What is the range?

The graph of





We need to find the lowest point on the graph.

We use the derivative:



and set it equal to 0:





; 

Solve that by the quadratic formula:



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

We substitute  in

  and after much work, we get

 so the range is



Edwin