Question

T(p)=(p-0.5)(1000/1-p^2)

p∈{0.5,∞)
Find all the critical points.
b- Find Extreme values and Absolute Extreme values.
c- Determine the behavior of function in the given interval.
d- What happened as p tends to infinity i.e.

e- Sketch the graph using information from a to d points.

Answer 1

Explanation:

T' = 1000(p^2 - 1 + 1)/(p^2-1)^2

(a) since T' is never zero, there are no maxima or minima.

However, there are asymptotes at p = -1 and p=1

(b) no extremes

(c) on [0.5,1) T increases to ∞

on (1,∞) T increases from -∞ to 0

(d) y=0 is the horizontal asymptote

there are lots of handy online graphing sites.