The following quadratic function is given: f(t) = 5t - 7t + 25. i) ii) iii) i) iv) Let g(t) = tf(t). Find g(t), then find the derivative of g(t) by using the rule of differentiation, and finally find g'(0). b) ii) iii) iv) ii) a) A soccer ball kicked up into the air is modelled by the following quadratic equation: y = 98t - 7t Use first principle to find the derivative of the function. where y shows feet above the ground t seconds after it is kicked. Find f(5) and f'(5). distance. Find the value of t when f'(t) = 25. Find the distance above the ground after 13 seconds. Find the value(s) of t when the ball is on the ground, i.e. y = 0. Graph the above equation on a pair of axes, showing all intercepts and the coordinates of the highest point reached by the ball. Find the time when it reaches the highest vertical distance and calculate this i) fencing wire. A farmer wants to put a fence around a rectangular paddock which is part of his block (see diagram below). Only three sides must be fenced since the fourth side is already fenced by his neighbour farmer as part of the border between the two blocks. The Farmer has 560 metres of fencing wire. X Already fenced x y Write an equation of the perimeter needing fencing with 560 metres of Write an equation for the area of the paddock only in terms of the side x. iii) Find the maximum area for the paddock if using only 560 metres of fencing wire for the three sides.