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 power and polynomial functions, including negative or fractional powers, and evaluate the derivative at a specified input.
Use first and higher derivatives to find gradients, rates of change and the derivative of a derivative in algebraic or function-graph contexts.
Use a derivative condition such as a specified gradient, stationary point or point of inflexion to determine an unknown parameter.

Learn this topic

Study SL 5.3—Derivative of powers conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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

Learn this topic

IB Maths AA SL 5.3 Derivative of Powers Questions question 1

Question (a)

Question (b)