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Date May 2013 Marks available 2 Reference code 13M.1.sl.TZ1.15
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 15 Adapted from N/A

Question

Consider the function f(x)=ax33x+5, where a0.

Find f(x).

[2]
a.

Write down the value of f(0).

[1]
b.

The function has a local maximum at x = −2.

Calculate the value of a.

[3]
c.

Markscheme

f(x)=3ax23     (A1)(A1)     (C2)


Note: Award a maximum of (A1)(A0) if any extra terms are seen.

a.

−3     (A1)(ft)     (C1)


Note: Follow through from their part (a).

b.

f(x)=0     (M1)


Note: This may be implied from line below.


3a(2)23=0     (M1)

(a=)14     (A1)(ft)     (C3)


Note: Follow through from their part (a).

c.

Examiners report

Many candidates could find the derivative of the cubic function and find the value of the derivative at x=0. For part (c) many candidates calculated the value of the function rather than the derivative at x=2.

a.

Many candidates could find the derivative of the cubic function and find the value of the derivative at x=0.

b.

Many candidates could find the derivative of the cubic function and find the value of the derivative at x=0. For part (c) many candidates calculated the value of the function rather than the derivative at x=2. However only the best realized that the derivative is zero at the maximum and so calculated the value of a.

c.

Syllabus sections

Topic 7 - Introduction to differential calculus » 7.2 » The derivative of functions of the form f(x)=axn+bxn1+, where all exponents are integers.
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