LIMIT AND DERIVATIVE QUESTIONS (25 marks) 1) Complete the following table. 2) Before completing the final column, vary the value of 'h' in the expression f(X + h) -f(x) and h then complete the table by hypothesizing a value for f' (x) as 'n' approaches zero. X f ( x ) = x ( x, f(x) ) h f(x+h) f ( x + h) -f(x) f ( x + h)- f(x) h f' (x) = lim h-0 h -2 -1 O 2 3) Graph f(x) = x2. 4) How do the values in the final column of the table relate to the graph of f(x)? 5) Sketch the tangents to f(x) at each point plotted on the graph. 6) By using the x-coordinates given, and the entries in the final column of the table, graph the derivative of f(x) on a separate grid