The path of a total solar eclipse is modeled by

f left parenthesis t right parenthesis equals $0\mathrm{.}00337$ t squared minus $0\mathrm{.}469$ t plus $19\mathrm{.}338$f$($t$)=0\mathrm{.}00337$t$20\mathrm{.}469$t$+19\mathrm{.}338,$

where$$ f$($t$)$ is the latitude in degrees south of the equator at t minutes after the start of the total eclipse. What is the latitude closest to the$$ equator, in$$ degrees, at which the total eclipse will be visible.

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Part $1$

The latitude closest to the equator at which the total eclipse will be visible is