Assignment 1
[Submission deadline: 24 Oct 2017]
Question 1
A company produces toys, the cost (C) and revenue function (R) are given
below whereas the revenue function depends on the number of toys (q).
What is the production level when the profit is maximized?
,004.05.1500000,15)( 32 qqqqC
2
61600)( qqqR
Question 2
Starting with the graph of
xxf 2ln)(
, find the equation of the graph
that results from
(a) shifting 3 units upward
(b) shifting 3 units to the left
(c) reflecting about the x-axis
(d) reflecting about the y-axis
Question 3
A boat is moving at a speed of 25 km/h along a straight shoreline. The boat
is 5 km from shore and it passes a lighthouse at noon.
(a) Express the distance s between the lighthouse and the boat as a
function of d, the traveled distance of the boat since noon; that is,
find f so that s = f(d).
(b) Express d as a function of t, the time elapsed since noon; that is, find
g so that d = g(t).
(c) Find f(g(t)). What does this function represent?
Question 4
Since light travels much faster than sound, you see the lightning before you
hear the thunder during a thunderstorm. The distance between you and the
storm varies directly as the time elapsed between the lightning and the
thunder. Suppose that the thunder from a storm 1.8 miles away from you
