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The path of a total solar eclipse is modeled by f(t) = 0.00302t^2 - 0.516t +...

The path of a total solar eclipse is modeled by f(t) = 0.00302t^2 - 0.516t + 40.984, 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.

The latitude closest to the equator at which the total eclipse will be visible is ___degrees S. (Round the final answer to two decimal places as needed. Round all intermediate values to four decimal places as needed.)

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Answer #1

We have to find the critical point of the function f(t), by putting f'(t)=0 and then solving for t. By using the second derivative test, we will prove our result, as explained in the solution.

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