+128475 Let's take this a little at a time
a) x is the number of hours after midnight
b) f(x) is the temp in Celsius
c) Note that 24 represents the number of hours in a day....we don't need any more that that !!!!
d) Here's the graph : https://www.desmos.com/calculator/foicqsv1oh
e ) Looking at the graph.....the coldest temp occurs at the low point on the graph ....the graph shows that the lowest temp occurs at (14.-10)
This means that the coldest temp of -10C occurs 14 hours after midnight = 2 PM
The warmest temp occurs (strangely) at midnight (t = 0) !!!...this is the highest point on the graph...the temp at this time is 9.6C
f) The graph shows that the temp decreases from midnight to 2PM
To find the avg rate of decrease we have
[ temp at midnight - temp at 2PM ] / [ 0 - 14 ] =
[ 9.6 - (- 10) ] / [ 0 - 14 ] = 19.6 / -14 = -1.4
This means that the temp is falling 1.4C every hour
g) The temp increases from 2 PM to the next midnight (where it is 0C )
So...the average rate of increase is
[ temp at next midnight - temp at 2PM ] / [24 - 14 ] =
[ 0 - (-10) ] / [ 10 ] = 1
This means that the avg rate of increase = 1C per hour
