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)
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
