Topic name: Related rates and l hopital rule

Hi, Please assist me with these questions. Solve them in an easy and thorough method (Step By Step). Please make sure to capture your work through a cam scanner and send it.

1. A particle moves on the hyperbola xy=18 for time t20 seconds. At a certain instant, y=6 and -=8. Which of the following is true about x at this instant? a) x is increasing by 4 units per second. b) x is decreasing by 4 units per second. c) x is decreasing by 1 unit per second. d) x is increasing by 1 unit per second. 2. Suppose that x and y are differentiable functions of t and are related by the equation 3x2 =2y? + 4. Given that= tax = -1, find " when (x, y) = (-2, 3), so dx at a) -2 b) -1 W H 3. A local automobile dealer has found that advertising produces sales, but that too much advertising tends to "turn consumers off," resulting in reduced sales. On the basis of past experience, the dealer expects that the number V ( x ) of vehicles sold during a month is related to the amount spent on advertising by the function below. V(x) = - 0.1x3 + 2.2x2 + 1.2x + 15 (0 S x S 20), Where x is the amount spent on advertising (in tens of thousands of dollars). What is the point of diminishing returns? Hint: The point of diminishing returns is the inflection point a) (7.33, 102.58) in tens of thousands dollars b) (7.33, 452.22) in tens of thousands dollars c) (7.33, 712.14) in tens of thousands dollars d) (7.33, 911.56) in tens of thousands dollars