PRISCILLA BAHA!! minating Task Part 1- Thinking and Communication Dec 2021 1. An open topped box can be made from a sheet of aluminum measuring 50 cm by 30 cm by cutting four congruent squares from each corner and folding up the sides. The volume of the box is 4000 cm3. a) Determine a polynomial function representing the volume of the box b) Determine the side length(s) that are possible for the square cut-outs. Round to two decimal places if needed. 2. The function f(x) = ax3 - x2 + bx - 24 has three factors. Two of these factors are x - 2 and x + 4. Determine the values of a and b, and then determine the other factor. (NO DECIMALS) Determine the equation of the quartic function with zeros at x = - , 0, and 2. The zero at x = 2 is a turning point on the graph and the function passes through (-1, -9). 4. Given f (x) = x - 2 x + 2 , find the equation of the inverse function f-1 (x) 5. A soccer ball is kicked into the air such that its height, h, in metres after t seconds is given by the function h (t ) = -4.9+2+ 14.7t + 0.5. a) Using the difference quotient, determine the equation for the slope of the tangent (hint: make h=0 at the end) b) Determine the slope of the tangent at 1.5 seconds. What does this mean? C) Determine the equation of the tangent line at 2.1 seconds. d) Determine the instantaneous speed at 2.1 seconds