March 26

3.1.  Derivatives of Polynomials and Exponential Functions

objective:

• to understand how derivatives of some basic functions were derived
• to understand how the definition of e was derived

• derivatives of a constant function, the power rule, constant multiple rule
• sum and difference rules
• derivative of e^x

solved problems - using key ideas

• students at board, #3-15 odd, 17-20
• using the calculator to compare f(x) and f'(x), #24
• equation of tangent line, #32
• exponential function and its derivatives, #1
• first and second derivatives, #34
• velocity, #38
• modeling population growth, #39
• where is the function increasing?  concave up?, #42
• finding tangent lines from a point outside of the curve, #47
• normal line, #49
• nth derivative of a function, #52
• limits, #59

group work
none

announcements
Homework. #2,16,22,32,40,54
 
 
 

QUESTION OF THE DAY

If  and f'(x) is positive for all x, what is ?

SOLUTION

SOLUTION.  Since f'(x) is positive, f(x) is increasing.  Since  the line y = 100 acts as an asymptote and