(c) Calculate the value of for which the gradients of the two graphs are the same. x 2 marks (d) Draw the tangent to the parabola at the point with the value of found in part (c). x 2 marks Question 7 Consider the function = + , 0. f(x) x3 x ≠ (a) Calculate f(2). 2 marks (b) Sketch the graph of the function = for 5 and 200. y f(x) x y –5≤ ≤ –200 ≤ ≤ 4 marks (c) Find f′(x).
(c) Calculate the value of x for which the gradients of the two graphs are the same. 2 marks (d) Draw the tangent to the parabola at the point with the value of x found in part (c). 2 marks Question 7 Consider the function f(x) = x3 + , x ≠ 0. (a) Calculate f(2). 2 marks (b) Sketch the graph of the function y = f(x) for –5≤ x ≤ 5 and –200 ≤ y ≤ 200. 4 marks (c) Find f′(x).
Differential-Calculus-Test-2016.docx