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#### DeusAbscondus

##### Active member

- Jun 30, 2012

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This problem is from a trial test (the main test is in one week's time)

Quickly for some background to what I have done maths-wise:

1. a crash course in college level maths in the first semester of Australian academic year: (february 2012 to June 2012) followed by crash course in calculus (july till now) This, just to give you an idea of the level I'm at.

Here is the question/problem, verbatim:

"Data has been recorded over the past 10 years measuring the quantity of litter, Q, removed from a particular park. Over the period $$\frac{dQ}{dt} \text{ is less than 0 and} \frac{d^2Q}{dt^2}\text{ is greater than 0 }$$

i) Draw a neat sketch of Q against t over the last 10 years.

ii) What conclusions can be drawn about the amount of litter over this period?

I deduce from this that:

1. $f(x)$ must slope negatively for the 10 year period (placing the tangent curve below the x-axis) as f'(x) has been less than zero for that period; and

2. the concavity has been positive for the entire period (f''(x) is greater than zero) meaning that f(x) is bending concave up the whole of this time.

Finally, to graph f(x), I chose an abitrary point (what choice did I have here?) up the Q axis, and sketched part of a concave up parabola (a curve whose slope is decreasing, decreasingly) curving down towards Q=0 at point t=10.

Question 1: am i justified in my first 2 assumptions?

Question 2: would my graph be a fair representation of what we know from the problem?

Question 3: is there any reason to support the hypothesis that f(x) is quadratic, f'(x) linear negative and f''(x) positive constant?

thanks guys,

Deus Abs

PS Latex for "less than" and "greater than" ?