Find the second derivative of the following functions: (a) f(x): x4 - sinx (b) f(x): sin(x2) (C) f(X) = 64\" Marks: 4 Find the derivative of the following functions: a. f(x) = (23c3 + 3)(8xZ + 4) b. f(x) = (4x + 2)3 8x4+2x14 - W) = W Marks: 4 Evaluate the following limits: 3 lim x2+1 Ex+32 ' \"\"4 x+4 . x2 +12x+32 b. 11111;\"... 4 - 1+4 What is the equation of the tangent to f (x) = 3x1 + 2x 14, where the slope of the tangent is 4? Marks: 4 Use rst principles to nd the derivatives of the following functions. Confirm your work by using the derivative shortcuts. a. for) = 3x2 + 2x 14 A rancher has 1000 m of fencing to enclose two rectangular corrals. The corrals have the same dimensions and one side is common. What dimensions will maximize the enclosed area? X XAn electronic store in selling CD players with a regular price of $90. During a typical two weeks the store sells 50 units' Past sales indicate that for every $1 decrease in price the store sells ve more units during two weeks. Calculate the price that will maximize revenue. Marks: 4 The operating cost, C in dollars per hour, for an airplane cruising at a height of h metres and an air speed of 200 km/h is given by C = 4000 + h/15 + 15000000/h for the domain 1000