Difference between revisions of "Practice problems/A photographer at the skatepark"
From UBCMATH WIKI
| Line 1: | Line 1: | ||
| − | [[Image:halfpipe.png|thumb|<caption>'''Figure 1'''. The shape of the half-pipe, | + | [[Image:halfpipe.png|thumb|<caption>'''Figure 1'''. The shape of the half-pipe, $h(x)$, with camera at height $c$.</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 | ||
| − | + | $$h(x)=x^3-6x^2+11x-6$$ | |
| − | where | + | 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.] | [This problem is a bit tricky.] | ||
Latest revision as of 13:43, 11 June 2014
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.]
