Applied Derivatives
Practice
For practice answer the following.
2.1 
a) Find the instantaneous velocity at 1 second.
b) Find the average acceleration from t = 1 second to t = 3 seconds.
c) Find the instantaneous acceleration at t = 4 seconds
2.2 A particle moves along the x-axis with its position determined by 
a) For what values of f (f > 0) is the particle at rest?
b) On what interval is the particle moving to the left?
Test the velocity between 0 and 4 seconds and then after 4 seconds. If velocity is negative then the object is moving to the left and this is the correct interval. If velocity is positive then its moving to the right and this is the incorrect interval.
moving to the right
moving to the left
Between 0 and 4 seconds the particle is moving to the left.
c) How far does the particle travel from t = 0 to t = 6?
This problem must be broken down to the intervals where it is going in one direction. Calculate distance traveled from 0 to 4 seconds and then add the distance traveled from four to six seconds.
f(x) = t² -8t +3
f(0) = 0² - 8(0) + 3 f(4) = 4² - 8(4) + 3 f(6) = 6² - 8(6) + 3
f(0) = 3 f(4) = -13 f(6) = -9
|3 – (-13) | = 16 |(-13) - (-9)| = 4
16 + 4 = 20.
Note the absolute value signs because it is impossible to have a negative distance.
2.3 Let 
a) Find f`(x)
b) Write the equation of the tangent line at x = 3
2.4 Given 
a) For what values of x does the f(x) have tangent lines that are horizontal?
b) Give the equations of the tangent lines in a)
2.5 Given 
a) Find 
b) Find 
