please help me solve this problem

x24 E 3 1) Given f(x): x 2(x2 16) ll 3x3 Hence, nd all the stationary points. a. Show that f '( x) = by using the quotient rule. b. Using the second derivative test, determine the relative minimum and maximum for the curve f (x) at all stationary points. 2) Find the equation of the 110mm] line for the curve y = :Jc3 + 3x2 + 4 at x =1 3) A parabola is dened as y = d7x+ 5 . A point (3,0) is located near the parabola. Show that x = % to get the shortest distance between the parabola and the point. 4) A piece of cardboard with 30cm length is to be bent as in Figure 1. Find the value of 6 for the shape to have largest area. (Reminder: sin2 9+ cos2 9 =1) .5) A giant tank in a shape of an inverted cone is lled with oil. The height of the tank is 1.5 metre and its radius is 1 metre. The oil is dripping at the bottom of the tank at the constant rate of 120cm3/s . Find a. Find the rate of change for the oil's radius when the radius is 0.4m b. Hence, calculate the rate of change for the oil's height when the height is 15cm c. A circular oil slick formed with uniform thickness from the drip. Assuming the thickness of the oil slick is always constant at 0.1cm, nd the rate of the oil's radius when the radius is 10 cm. 6) A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 4 ft/sec. After 12 seconds, how rapidly is the area disturbed by the ripple increasing