IB Maths AA SL 5.3 Derivative of Powers Questions

Practise differentiating integer powers and sums of power terms, identifying the correct derivative rule and checking the resulting function or rate of change.

Exam points

Differentiate f(x) = ax^n for integer n using f′(x) = anx^(n−1), including negative and zero powers where defined.
Differentiate sums of integer-power terms term-by-term and simplify the resulting derivative for use in a stated problem.

[Maximum number: 6]

Part of the graph of $f(x)=a x^{3}-6 x^{2}$ is shown below.

Figure for Question IB Maths AA SL 5.3 Derivative of Powers Questions question 1 — IB Maths AA SL

The point P lies on the graph of f. At P, x=1.

(a)

Find $f^{\prime}(x)$ .

[ 2 ]

$f^{\prime}(x)=3 a x^{2}-12 x$

Note: Award A1 for each correct term.

(b)

The graph of f has a gradient of 3 at the point P . Find the value of a.

[ 4 ]

setting their derivative equal to 3 (seen anywhere)
e.g. $\quad f^{\prime}(x)=3$
attempt to substitute x=1 into $f^{\prime}(x)$
e.g. $\quad 3 a(1)^{2}-12(1)$
correct substitution into $f^{\prime}(x)$
e.g. $\quad 3 a-12,3 a=15$
a=5
5. Note: All answers must be given in terms of m. If a candidate makes an error that means there is no m in their answer, do not award the final A1 F T mark.

METHOD 1

All question bank results loaded

IB Maths AA SL 5.3 Derivative of Powers Questions question 1

Question (a)

Question (b)