Question 1 [6] Determine the derivatives of each of the following 1.1. y = = _sin x cosx using quotient rule (2) 1.2. y = ex +ze-3x - 2ax (2 ) 1.3. y = x3 In (5x - 1) (2) Question 2 [12] Determine the - and x 2.1. y = VI-XZ (4) 2.2. y = e2x sin (2nx) (4) 2.3. The displacement, x of a particle is given by x = te-t. Determine the velocity, v = = and the acceleration, a = d2x at 2 (4) Question 3 [6] Determine the 3.1. exy = e4x - e5y (3) 3.2. Given that x2 - xy + 2y2 = 9, evaluate dy at (3;1) (3) Question 4 [8] Let f (x) = =x4 - 2x3 - 4x2+ 2x+1 a. Determine the turning points of the function f (2) b. Use the second derivatives to determine the minimum and maximum turning points. ( c. Sketch the graph of the function f (4) FORMULA SHEET FOR HEMSX3A y = f(x) dy k (any constant) 0 axn naxn-1 ef (x) f'(x )ef (x) af (x) f'(x )af(x) Ina Inlf (x)| f (x) f(x) f(x) > 0] loga f(x) f' (x) f (x) In a f(x)]" nif(x) ]n-if' (x)