IB Maths AA HL 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.

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Question 1

Paper 2, calculatorHard6 marks

Let $n$ be a fixed positive integer and let $f(x)=x^n$ where $x\in\mathbb R$

(a)

Using the definition of the derivative from first principles, show that

f'(x)=nx^{n-1}.

[3]

(b)

For an integer $r$ with $1\le r\le n$ prove that

f^{(r)}(x)=\frac{n!}{(n-r)!}x^{n-r}.

[3]

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