1. (This is the slope of our tangent line…)
Power Rule continued…
ex: Find the equation of the tangent line to the curve
(This is the slope of our tangent line…)
Equation of the tangent line: y – y1 = y’(x – x1) :

2. Constant Multiple Rule
Sum/Difference Rule
ex:
ex:
ex: Find the points on curve y = x4 – 6x2 + 4 where a tangent line would be horizontal…

3. ex: Position function s(t) = 2t3 – 5t2 + 3t + 4 (cm/sec)
Find acceleration as a function of time [a(t)], and…
Find the acceleration after 2 seconds [a(2)]
OK… acceleration is the second derivative of position, so…
(Answer to #1)
(Answer to #2)

4. Definition of the Number e
e is the number such that:
lim
h-->0
y = ex m=
m = 1
(1, )
(0, 1)