The position of an object at time t is given by s(t) = -8 - 9t. find the instantaneous velocity at t = 1 by finding the derivative. using the limit formula to find the derivative

Ughhh...the limit formula...this should be thrown in the trash the minute you start doing derivatives :P

(-8-9(t+d)-(-8-9t))/(t+d-t)

(-8-9t-9d+8+9t)/d

-9d/d  (which is -9 for any value of d as well as when d approaches zero)

-9

So the instantaneous velocity is regardless of t or delta t

To obtain the minimum and maximum temperatures (x) for Lollypop Town, the equation can be simplified to obtain the missing variable:

2|x - 6| + 14 = 38
2|x - 6| = 38 - 14
2|x - 6| = 24
|x - 6| = 12

Simplifying |x-6| = 12 can be done in two ways:

A.)
|x - 6| = 12
x - 6 = 12
x = 18 (maximum temperature)

B.)
|x - 6| = 12
x - 6 = -12
x = -6 (minimum temperature)