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.

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Question 1

Paper 2, calculatorEasy6 marks

Consider the functions $f(x)=x^3-3x$ and $g(x)=x^3$

The stationary points of $f$ are $(-1,2)$ and $(1,-2)$

(a)

Use the second derivative test to classify each stationary point of $f$

[2]

(b)

Determine whether $(0,0)$ is a point of inflexion of $f$ and state the gradient there.

[2]

(c)

Determine whether $(0,0)$ is a point of inflexion of $g$ and state the gradient there.

[2]

Question 2

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]

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