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.

Paper

Paper 1, no calculator Paper 2, calculator

Difficulty

Easy Medium Hard

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]