The problem is...
Let f(x)= 5x^3 + kx^2 + 5x, k a constant. For what values of k is f one-to-one?
How would you work this problem to find what k is?
To be strictly increasing or decreasing we require that this derivative be either always positive or negative. Since the leading coefficient is positive it means this must be strictly increasing. This quadradic is positive when the discrimant is negative,
Solve for .