Distance formula

• Feb 22nd 2008, 10:55 AM
XIII13Thirteen
Distance formula
Distance: $\displaystyle s=-16t^2+800t$

find t, for s increasing, for s'=0, and for s decreasing

Am I figuring maximums and minimums here?

$\displaystyle y'=-32t+800$ =$\displaystyle y'=-t+25$

so I have a critical point at x=25

$\displaystyle y''=-1$

So our singular critical point is a maximum. So t>25 we start to decrease?

I have a multiple choice solution set

a.) (0,25]
increasing
{0,50}
s=0

b.)[25,50]
decreasing
{0,50}
s=0

c.) {0,50}
s=0

d.) None of these

Keep in mind. He likes to trick us and I've noticed a lot of "none of these" resulting from things like positive and negative signs in the equation. Part of the thing confusing me is how he wrote up the solution set
• Feb 22nd 2008, 11:19 AM
galactus
As you probably know, it is a concave down parabola with vertex at
V(25,10000).

It follows that $\displaystyle f'(x) < 0 \;\ if \;\ 25 < x < {\infty}$

and $\displaystyle f'(x) > 0 \;\ if \;\ {-\infty}<x<25$

Since f(x) is continuous at x=25:

Therefore it is decreasing over the interval $\displaystyle [25,\infty)$ and increasing over the interval $\displaystyle (-\infty, 25]$

$\displaystyle f''(x) < 0---->f''(x) = -32$, so it is concave down. We can tell that from the negative coefficient of x^2.
The text passage contains a mathematical problem involving the distance formula and its derivative to find intervals of increase and decrease, as well as a critical point. The problem is followed by an analysis and a multiple-choice solution set.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Distance formula

• Feb 22nd 2008, 10:55 AM
XIII13Thirteen
Distance formula
Distance: $\displaystyle s=-16t^2+800t$

find t, for s increasing, for s'=0, and for s decreasing

Am I figuring maximums and minimums here?

$\displaystyle y'=-32t+800$ =$\displaystyle y'=-t+25$

so I have a critical point at x=25

$\displaystyle y''=-1$

So our singular critical point is a maximum. So t>25 we start to decrease?

I have a multiple choice solution set

a.) (0,25]
increasing
{0,50}
s=0

b.)[25,50]
decreasing
{0,50}
s=0

c.) {0,50}
s=0

d.) None of these

Keep in mind. He likes to trick us and I've noticed a lot of "none of these" resulting from things like positive and negative signs in the equation. Part of the thing confusing me is how he wrote up the solution set
• Feb 22nd 2008, 11:19 AM
galactus
As you probably know, it is a concave down parabola with vertex at
V(25,10000).

It follows that $\displaystyle f'(x) < 0 \;\ if \;\ 25 < x < {\infty}$

and $\displaystyle f'(x) > 0 \;\ if \;\ {-\infty}<x<25$

Since f(x) is continuous at x=25:

Therefore it is decreasing over the interval $\displaystyle [25,\infty)$ and increasing over the interval $\displaystyle (-\infty, 25]$

$\displaystyle f''(x) < 0---->f''(x) = -32$, so it is concave down. We can tell that from the negative coefficient of x^2.
user
The text passage contains a mathematical problem involving the distance formula and its derivative to find intervals of increase and decrease, as well as a critical point. The problem is followed by an analysis and a multiple-choice solution set.

TYPE: SINGLE_QUESTION_WITH_ANSWER