Problem #PRU-111923

Problems Calculus Derivative Derivative and extrema Derivative and multiple roots

Problem

When water is drained from a pool, the water level $h$ in it varies depending on the time $t$ according to the function $h (t) = a t^{2} + b t + c$ , and at the time $t_{0}$ of when the draining is ending, the equalities $h (t_{0}) = h^{'} (t_{0}) = 0$ are satisfied. For how many hours does the pool drain completely, if in the first hour the water level in it is reduced by half?

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