\(\boxed{a = \frac{1}{2}, b = -\frac{1}{2}, c = 2}\)
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- \[ \frac{1}{2} - \frac{1}{2} + c = 2 \]
- \[ c = 2 \]
- Thus, the coefficients are \(a = \frac{1}{2}\), \(b = -\frac{1}{2}\), and \(c = 2\).
- A chemist is analyzing a reaction involving a catalyst and models the concentration of a reactant over time \(t\) with the function \(C(t) = \frac{kt}{t^2 + 1}\). Determine the time \(t\) at which the concentration is maximized.
- To find when \(C(t) = \frac{kt}{t^2 + 1}\) is maximized, find the critical points by setting the derivative \(C'(t)\) to zero.
- First, compute the derivative using the quotient rule:
