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Calc_review_4_-_3.4,_3.7,_4.6 - AP Calculus Review 3.4 3.7...

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AP Calculus Name: ________________________ Review 3.4, 3.7, 4.6 Position, velocity, acceleration Implicit Differentiation Related rates Differentiate each function with respect to x. 1. x y = 2 2. 7 2 2 = + - y xy x 3. 0 sin cos 2 2 = - y y x 4. Using the implicit relation ) 7 ( 2 2 + = x x y , a. Find dx dy by implicit differentiation. b. Find an equation for the tangent line to the curve at (-3, 6) c. Find any points where the tangent line is vertical (if it exists). 5. Consider the curve defined by 12 4 2 2 - = + + y xy x . (a) Find dx dy in terms of x and y. (b) Find the equations of all horizontal tangent lines.
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(c) Find the equation of the tangent line at the point (-4, 14) 6. While painting my houseatop a 25 foot ladder, I was horrified to discover that the ladder began sliding away from the baseof my homeat a constant rate of 2 ft/sec (don’t ask how I knew that, I just did). At what rate was the top of the ladder carrying me, screaming like a 2 year old, toward the ground when the baseof the ladder was already 17 feet away from the house?
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