Problem 4 (20 marks) A car's fuel consumption is given by C(s) = 10 + s litres per 100 km, where s is the slope of the road. For example, on a flat road, the consumption is C(0) = 10 litres per 100 km. On a road with downhill slope s = -1/2, the consumption is C(-1/2) = 9.5 litres per 100 km. (a) Consider the following stretch of road. 50km How much fuel will be consumed on the drive from x = A to x = B? (b) Now consider a mountain range whose shape is given by a differentiable function y = f(x). Both x and y are given in km. VA A B Determine the car's total fuel consumption in litres driving from x = A to x = B. Apply the five-step slicing method in complete detail. You may leave your final answer as a definite integral. Hint: it may be worth going over example 4.3 of the Week 6 lecture notes. (c) By choosing an appropriate function y = f(x) in part (b) recover your answer to part (a). Hint: let A = 0 so the car starts at the origin and find B