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Date May 2008 Marks available 2 Reference code 08M.2.sl.TZ1.5
Level SL only Paper 2 Time zone TZ1
Command term Justify Question number 5 Adapted from N/A

Question

The diagram below shows part of the graph of the gradient function, \(y = f'(x)\) .


On the grid below, sketch a graph of \(y = f''(x)\) , clearly indicating the x-intercept.

[2]
a.

Complete the table, for the graph of \(y = f(x)\) .

[2]
b.

Justify your answer to part (b) (ii).

[2]
c.

Markscheme

     A1A1     N2

Note: Award A1 for negative gradient throughout, A1 for x-intercept of q. It need not be linear.

[2 marks]

a.

     A1A1     N1N1

b.

METHOD 1

Second derivative is zero, second derivative changes sign.     R1R1     N2

METHOD 2

There is a maximum on the graph of the first derivative.    R2     N2

c.

Examiners report

Several candidates had a correct sketch in part (a).

a.

The majority of the errors occurred in parts (b) and (c). In part (b), some seemed to just guess while others left it blank.

b.

In part (c), justification lacked completeness. For example, many stated that the second derivative must equal zero but said nothing of its change in sign.

c.

Syllabus sections

Topic 6 - Calculus » 6.3 » Points of inflexion with zero and non-zero gradients.
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