For a positive number \(a\), let \[I(a) = \int_0^a \! \left(4 - 2^{x^2} \right) \, dx.\]

Then \(\dfrac{dI}{da}=0\) when \(a\) equals

\(\dfrac{1 + \sqrt{5}}{2}\),

\(\sqrt{2}\),

\(\dfrac{\sqrt{5} - 1}{2}\),

\(1\).

For a positive number \(a\), let \[I(a) = \int_0^a \! \left(4 - 2^{x^2} \right) \, dx.\]

Then \(\dfrac{dI}{da}=0\) when \(a\) equals

\(\dfrac{1 + \sqrt{5}}{2}\),

\(\sqrt{2}\),

\(\dfrac{\sqrt{5} - 1}{2}\),

\(1\).