1. 4:0 Compute the derivative f' (:13) where x) denotes the following functionsl: (a) ($2 rs) = sinus?) (b) (g) M) =1n(2r2 + 4) (c) (g) M) = mew) (d) (g) M) = 8M 2. 5 Identify all values of :1: for which the function at) = 11:4 + 62:3 + 12332 +63: + 2 is concave down. Use interval notation for your answer. 3. 3:0 Calculate 2% if 35' and y are related by the following equations given below. Here, both variables :1: and y will likely appear in your answer. (a) ($3 sinks + y) = 33 + 008(9) (b) ($11106) +1H(y) = I + y (c) (%) :1: (3/5 + y) arcsin(y + 3:) = a: . (On this problem, you may need to look up the derivative of arcsin($). I am explicitly not telling you because it is a genuinely useful skill to be able to learn to nd mathematical information on the internet yoursel\") 100 4. 2:0 Water pours into a conical tank (with tip touching the ground) which has total height 6 meters and radius 4 meters at a rate of 8%. At what rate is the water rising when the height is 5 meters high? (Hint: Use the fact that any cone of height h and radius T has volume m'g h.) Feel free to not do arithmetic