A scientist is watching a bug walk back and forth along a line. Suppose the line has a
coordinate x, and let p(t) be the continuous function giving the bug's position on the
line at time t (in sexonds).
The scientist oberves the bug's motions and records what she sces:
At t=0, the bug was bocated at x=-0.25.
At t=5, the bug passed through the point x=0 for the first and only time.
As t->infty , the bug approuches x=0. In other words, lim_(t->infty )p(t)=0.
The derivative funtion p^(')(t) - the velocity of the bug - is contimuous. For a few
seconds at the beginning p^(')(t) was negative, but then it crossed 0 to become positive
at t=3.3. It crossed 0 to become negative again at t=6.7, and remained negative
thereafter.
Also, p^(')(t) had its maximum value at t=5, and its most negative value at t=2.2
and t=7.8.
The bug always stayed within 5 units of x=0.
In this problem, you'll figure out how to sloctch a graph of the bug's movements on
the interval (0,infty ), even though you don't know the formula for p(t) ! For now, use the
information above to answer the following questions. (After you answer them all, you'll
get to make the slotch.)
(a) Where will the graph of p(t) intersect the t and x axes?
(b) Does the graph of p(t) have any asymptotes? If so, where are they?
(c) Wbere is p(t) increasing and where is it decressing?
(d) What are the t-coordiates of the local minima and maxima?
l. A scientist is watching a bug walk back and forth along a line. Suppose the line has a coordinate , and let p(t) be the continuous function giving the bug's position on the line at time t (in seconds)
The scientist observes the bug's motions and rexords what she sees:
o At t=0,the bug was located at r=-0.25. o At t=5, the bug passed through the point r =0 for the first and only time o As t oc, the bug approaches r = 0. In other words, lim,P(f) = 0. o The derivative funtion p(t) the velocity of the bug is continuous. For a few seconds at the beginning p(f) was negative, but then it crossed 0 to become positive at f = 3.3. It crossed 0 to become negative again at t = 6.7, and remained negative thereafter. o Also, p(f) had its maximum value at = 5, and its most negative value at t = 2.2 and = 7.8. o The bug always stayed within 5 units of r =0.
In this problem, you'll figure out how to sketch a graph of the bug's movements on the interval [0, c), even though you dont know the formula for p()! For now, use the information above to answer the following qucstions. (Affer you answer them all, you'll get to make the sketch.) (a) Where will the graph of p(t) intersect the and r axes?
(b Does the graph of p(t) have any asymptotes? lf so, where are they?
c Where is p increasing and where is it decreasing
(d What are the t-coordiates of the local minima and maxima?