IB Maths AA SL AA 5.1 Limits and 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

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Question 1

Paper 1, no calculatorEasy7 marks

The curve $C$ has equation $y=f(x)=(x+1)e^{x^2}$ where $x\in\mathbb R$ The curve passes through $(0,1)$

(a)

Determine $f'(x)$

[3]

(b)

Hence, determine the equation of the tangent to $C$ at $x=0$

[3]

(c)

The tangent meets the $x$ -axis at $P$ Find the $x$ -coordinate of $P$

[1]

Question 2

Paper 2, calculatorMedium6 marks

For $x\in\mathbb{R}$ let $f(x)=(x+2)e^{-x}$

(a)

Find $f'(x)$

[2]

(b)

Hence determine the coordinates of the local maximum of the curve $y=f(x)$ justifying that it is a maximum.

[4]

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