THE DERIVATIVE FUNCTION
(Applications)
Example 
An object moves in a straight line with its position function at time
t seconds given by s(t) = t2 – 3t + 5, t  0, where s is measured in metres.
Determine the velocity of the object at t = 0s and t = 2s.
TANGENT LINES and NORMAL LINES
The normal to the graph of a function,
y = f(x), at point, P, is the line that is
perpendicular to the tangent at P.
Note:
 slopes are equal
 slopes are –ve reciprocals
Consider the function, f ( x )  x , x  0.
Example 
a)
Determine f '( x ) .
f '( x )  lim
h0
f ( x  h)  f ( x )
h
Note: the derivative may
not be defined over the
function’s entire domain.
b)
Determine the equation of the normal to f(x) at x = 1.
c)
Determine the equation of the tangent to f(x) that is parallel to x – 4y + 1 = 0.
Homework: p.74–75 #10, 11, 14, 19, 20