please help answer practise exam questions thank you.

601 6012 Question 6 (12 marks) a) Differentiate the following functions with respect to x. (Ensuring you use the correct notation) (1, 2, 2) (i) y = 5x + 4 (ii) f (x) = (3x-2)(1-x) (ini) h(x) = ax-bx3 2 cx for cand x * 0 b) For the function f(x) = x3+ 5 -7x+6. (i) Determine the coordinates of the point/s on the curve at which the gradient of the tangent to the f (x) is equal to 3. (4 marks) (ii) Find the equation of the tangent, in 'gradient-intercept form' to the curve of f(x) at the point where x = 1 (3 marks) (You may need to review 'Point-Gradient' form of a straight line) Question 7 (9 marks) a) Approximate the instantaneous rate of change of the function f (x) = x2 - 4x + 2, at the point where x = 7 by considering the secant between the points on the curve where x = 7 and x = 7.1 (3 marks) b) Calculate the gradient of the tangent to the curve when x = 7 , using a method of your choice. (2 marks) c) In a hypothetical scenario, the gradient of a secant PQ can be used to approximate the gradient of the tangent at P provided it is within 20% of the actual value. If P is the point on f (x) = x2 - 4x + 2 where x = 7, between what values of x can Q be located to ensure the secant gives an acceptable approximation for the tangent? (4 marks)