A research team models the fuel efficiency EEE of a prototype engine as a function of its operating speed vvv (where v>0v > 0v>0). The efficiency function is determined to be convex (also known as concave up) across its entire domain. Identify which of the following functions could represent E(v)E(v)E(v).
A: E(v)=40+15ln(v)E(v) = 40 + 15\ln(v)E(v)=40+15ln(v)
B: E(v)=v2+900vE(v) = \frac{v^2 + 900}{v}E(v)=vv2+900
C: E(v)=120+2v−0.05v2E(v) = 120 + 2v - 0.05v^2E(v)=120+2v−0.05v2
D: E(v)=200(1−e−0.2v)E(v) = 200(1 - e^{-0.2v})E(v)=200(1−e−0.2v)
57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.