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- September 24th 2008, 01:38 PM #1

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## Max or Min

The height of an object,

*h*(*t*), is determined by the formula

h(*t*) = –16*t*2 + 256*t*, where t is time, in seconds. Will the object reach a maximum or a minimum? Explain or show your reasoning.

I have trouble with questions like this when the value of the variable is not given.

How can I find the answer without having to graph the given function?

- September 24th 2008, 01:43 PM #2

- September 24th 2008, 05:22 PM #3

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- September 24th 2008, 05:26 PM #4

- September 25th 2008, 12:05 AM #5
No. But obviously if you're going to draw a graph their are features you try to calculate, including coordinates of the turning point. You don't have to draw the graph to get the coordinates.

Using symmetry, the t-coordinate of the turning point lies half-way between the t-intercepts. Do you know how to find it. Once you have the t-coordinate of the turnng point, how to get the h-coordinate shuld be clear. And it's a negative parabola (coefficient of squared term is negative). So the turning point is a maximum.

- September 25th 2008, 02:14 AM #6

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You are not asked to find the maximum or minimum, but just to identify if the given function has a max or min.

You should recognise that h(t) is a parabola opening downwards, and hence this has a maximum. Also you should know that the maximum occurs midway between the roots, which in this case are obvious.

RonL

- September 25th 2008, 05:40 AM #7

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- September 25th 2008, 06:39 AM #8

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- September 25th 2008, 01:41 PM #9

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- September 25th 2008, 01:43 PM #10

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- September 25th 2008, 01:44 PM #11

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- September 25th 2008, 01:45 PM #12

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- September 25th 2008, 01:50 PM #13

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- September 25th 2008, 01:51 PM #14

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- September 25th 2008, 05:44 PM #15