Stimulus: random point on function graph

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Alexander Holvoet 9 months, 3 weeks ago

Published this.

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Alexander Holvoet 9 months, 3 weeks ago

Created this as a copy of Finding point on a graph with given derivative.

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Question statement

Given below is the graph of a function $y=f(x)$ .

{graph_cubic(a,b,c,d)}

Give any introductory information the student needs.

			Name	Type	Generated Value

cubic_coefficients	list	[ -1/16, 1/16, 1/16, -1/16 ]
quadratic_coefficients	list	[ 1/2, -1/2, -1/4, 1/4 ]
linear_coefficients	list	[ -1/4, 1/4, -3/4, 3/4 ]
constants	list	[ -1, 6, 2, 3 ]
pick_curve	integer	3
a	rational	-1/16
b	rational	1/4
c	rational	3/4
d	integer	3
x0	integer	4
y0	rational	6
y0prime	rational	-1/4
ch	list	[ -2, 2, 3, 4, 6, 7 ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[-1/16,1/16,1/16,-1/16]

JME function reference

Description

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

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Generated value: `list`

[ -1/16, 1/16, 1/16, -1/16 ]

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Choose one from a list
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Gap-fill

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

For $x=$Unnamed gap , $f'(x)=\var{y0prime}$.

Advice

The derivative at $x$ corresponds to the slope of the tangent line to the graph at the point $(x,f(x))$. In the figure below, we have drawn the line with slope $\var{y0prime}$ through the origin in blue. We have also drawn a tangent line (in red) to the graph that is parallel to it and where the point of tangency has an $x$-value from the choices offered.

{graph_cubic_and_lines(a,b,c,d,x0,y0,y0prime)}

We see that the correct choice is $\var{x0}$.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Alexander Holvoet 9 months, 3 weeks ago

Alexander Holvoet 9 months, 3 weeks ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

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Stimulus: random point on function graph

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Alexander Holvoet 9 months, 3 weeks ago

Alexander Holvoet 9 months, 3 weeks ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`