SOLUTION: As you know my brother Jim is an avid fisherman. He varies the depth at which he fishes according to the following function: D(t) = -t2 + 10t where t is measured in hours. Estim

Question 204671: As you know my brother Jim is an avid fisherman. He varies the depth at which he fishes according to the following function: D(t) = -t2 + 10t where t is measured in hours. Estimate the time when he fishes at the greatest depth and tell me that depth.

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Given the function for depth, D, as a function of time, t, in hours, find the time at which the depth is greatest:
If you were to graph this function, the curve would be a parabola that open downward. the greatest point would be a maximum occuring at the vertex of the parabola.
The value of t at the vertex is given by:
where, in your equation, b = 10 and a = =1, so...

hours.
The maximum depth at time t = 5 is:

Meters, feet, fathoms, ...?

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