Turning points

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Frank Doheny

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From users who are not members of Introduction to differentiation :

Jo-Ann Lyons

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Ready to use

6 years, 2 months ago

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Jo-Ann Lyons 6 years, 2 months ago

Gave some feedback: Ready to use

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Frank Doheny 8 years, 5 months ago

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Frank Doheny 8 years, 7 months ago

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Name	Status	Author	Last Modified
Turning points	Ready to use	Frank Doheny	13/03/2019 15:21
Katy's copy of Turning points	Ready to use	Katy Dobson	09/01/2024 11:42
Simon's copy of Turning points	draft	Simon Thomas	14/03/2019 11:07
Turning points	draft	Xiaodan Leng	10/07/2019 22:14

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Question statement

The function $f(x)=2x^3-\simplify{3*({a}+{b})x^2+6*{a}*{b}x}+\var{c}$ has two turning points.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	2
b	integer	6
c	integer	10

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Input the smaller of the two $x$ values.

$x=$ Gap 0.

Input the larger of the two $x$ values.

$x=$ Gap 1.

Advice

$f(x)=2x^3-\simplify{3*({a}+{b})x^2+6*{a}*{b}x}+\var{c}$

To locate a turning point, differentite the function, set equal to zero and solve.

$f'(x)=6x^2-\simplify{6*({a}+{b})x+6*{a}*{b}}=0$

Divide across by 6 to get the quadratic equation

$x^2-\simplify{({a}+{b})x+{a}*{b}}=0$

This has factors

$(x-\var{a})(x-\var{b})=0$

$x-\var{a}=0$ or $x-\var{b}=0$

$x=\var{a}$ or $x=\var{b}$

Give a worked solution to the whole question.

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Part	Test	Passed?
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Number entry
Number entry		Hasn't run yet
Number entry
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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Jo-Ann Lyons 6 years, 2 months ago

Frank Doheny 8 years, 5 months ago

Frank Doheny 8 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Turning points

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jo-Ann Lyons 6 years, 2 months ago

Frank Doheny 8 years, 5 months ago

Frank Doheny 8 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`