Difference between revisions of "Practice problems/A photographer at the skatepark"
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[[Image:halfpipe.png|thumb|<caption>'''Figure 1'''. The shape of the half-pipe, <math>h(x)</math>, with camera at height <math>c</math>.</caption>]] | [[Image:halfpipe.png|thumb|<caption>'''Figure 1'''. The shape of the half-pipe, <math>h(x)</math>, with camera at height <math>c</math>.</caption>]] | ||
A photographer is taking pictures at a skatepark. The [[Wikipedia:Half-pipe|"half-pipe"]] has the shape of a function given by | A photographer is taking pictures at a skatepark. The [[Wikipedia:Half-pipe|"half-pipe"]] has the shape of a function given by | ||
| − | :<math>h(x)=x^3-6x+11x-6</math> | + | :<math>h(x)=x^3-6x^2+11x-6</math> |
where <math>x</math> is the horizontal distance from the photographer and <math>h(x)</math> is the height of the half-pipe surface above the point <math>x</math> (see Figure 1), both measured in tens of meters. The photographer has his camera mounted on a tall rod. He would like to hold the camera at a height <math>c</math> that is high enough so that there is no part of the half-pipe hidden from view. What is the minimum value of <math>c</math> for which this will be the case? | where <math>x</math> is the horizontal distance from the photographer and <math>h(x)</math> is the height of the half-pipe surface above the point <math>x</math> (see Figure 1), both measured in tens of meters. The photographer has his camera mounted on a tall rod. He would like to hold the camera at a height <math>c</math> that is high enough so that there is no part of the half-pipe hidden from view. What is the minimum value of <math>c</math> for which this will be the case? | ||
[This problem is a bit tricky.] | [This problem is a bit tricky.] | ||
Revision as of 11:00, 2 October 2013
A photographer is taking pictures at a skatepark. The "half-pipe" has the shape of a function given by \[h(x)=x^3-6x^2+11x-6\] where \(x\) is the horizontal distance from the photographer and \(h(x)\) is the height of the half-pipe surface above the point \(x\) (see Figure 1), both measured in tens of meters. The photographer has his camera mounted on a tall rod. He would like to hold the camera at a height \(c\) that is high enough so that there is no part of the half-pipe hidden from view. What is the minimum value of \(c\) for which this will be the case?
[This problem is a bit tricky.]
