SOLUTION: A ladder 4m long at a construction site is resting against a wall. The bottom of the ladder is slipping away from the wall. Find the estimate of the instantaneous rate of change of

Question 1174206: A ladder 4m long at a construction site is resting against a wall. The bottom of the ladder is slipping away from the wall. Find the estimate of the instantaneous rate of change of the Height H of the top of the ladder with respect to the Distance D of the bottom of the ladder from the wall when the bottom of the ladder is 2.5m away from the wall. Use h = 0.01 and the central interval.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The equation relating the height on the wall to the distance away from the
wall is: H = sqrt(L^2 - D^2), where L = the length of the ladder (a constant)
We need to find the rate of change of this function over the interval
D = [2.5-h,2.5+h]: deltaD/deltaH = [sqrt(L^2 - (D+h)^2) - sqrt(L^2 - (D-h)^2)]/2h
deltaD/deltaH = (sqrt(16-2.51^2) - sqrt(16-2.49^2)/0.02 -> -0.8006 ~-0.8
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