I not able to solve this question. Can show me step how you reach to answer

2. Consider the following related rates problem: An inverted conical tank (tie. a tank in the shape of a cone opening upwards) is being lled with water. The tank itself has a radius of 3ft and a height of 8ft, and the water is being poured into the tank at a rate of %ft3/min. Unfortunately, there is a small hole in the bottom of the tank that causes water to leak out at a rate of ft'l/min. How quickly is the height of the water in the tank changing when the tank contains Eft3 of water? Solve the related rates problem by completing the following steps: (a) Draw and label a picture. (b) Write down what you want to nd (a rate), and a list of what you are given. (0) Come up with an equation relating the quantities whose rates are described in the previous step. (Hint: Your equation will likely include the radius 'r' and height h of the water in the tank. Use similar triangles to nd a relationship between these to eliminate one of them from your equation.) ((1) Determine the value of the rate you are asked to nd. 3. Consider a scenario in which a 20ft tall lamppost lights up a street. (a) A 5ft tall woman stands close to the lamppost and the lamppost casts her shadow on the ground in front of her. If she walks away from the lamppost at a constant speed of 2ft /s, how quickly will the length of her shadow change? (b) Now suppose two people, one shorter than the other, walk away from the lamppost at the same constant speed 1:. Whose shadow is increasing faster, the taller person's or the shorter person's? and asks for your feedback. Write at least 30 words outlining the mistake(s) your friend has made in their solution and how your friend's solution could be improved overall (e. g. could your friend do something to make their solution easier to understand?) You may also want to point your friend in the right direction with regard to their mistakes (without going into too much detail). Question: Find the global maximum and minimum values of f (x) = We\" on the interval [17 ll ' Friend's solution: Using the Product Rule, we have that 1 \" 1 fl(x) = _m2/36:c _ x1/3em _ 6 ( 3x) 3 3552/3 , so f'(x) = 0 when a: = $7. Therefore, the global maximum is x = 1 and the global minimum is :c = 1