SOLUTION: Jim is an avid fisherman. He varies the depth at which he fishes according to the following: D(t)=-t^2+10t where t is measured in hours. Estimate the time when he fishes at the gre

Question 202718: Jim is an avid fisherman. He varies the depth at which he fishes according to the following: D(t)=-t^2+10t where t is measured in hours. Estimate the time when he fishes at the greatest depth and tell me that depth.

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
To start with, it helps if you can recognize the equation of D(t) as being the equation of a parabola, because of the t^2 term, which opens downward, because of the negative coefficient in front of the t^2 term. A graph of this equation is provided below.

From looking at this we can tell that the maximum depth (the highest value of D(t)) will be the vertex of the parabola. For parabolas in general the x-coordinate of the vertex can be found at where "a" and "b" are taken from the standard form for a parabola: .

In your equation the "a" is -1 and the "b" is 10. So the x-coordinate of the vertex is

So the maximum depth will be when the hour is 5 and the maximum depth will be D(5):

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