IB Maths AA HL AA 5.2 Applications of differentiation questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1, no calculator Paper 2, calculator

Difficulty

Easy Medium Hard

Question 1

Paper 2, calculatorHard6 marks

A manufacturer models the permitted side lengths $x$ and $y$ in metres, of a rectangular mounting panel by

x^2+xy+2y^2=36.

The positive value of $y$ is used, and installation requirements restrict $x$ to $4\leq x\leq 5$ The area of the panel is $A=xy$

(a)

Determine $\dfrac{dy}{dx}$ in terms of $x$ and $y$

[2]

(b)

Hence, or otherwise, determine the maximum possible area of the panel on the allowed interval.

[4]