Unit 2

Question 0

Alternate definition of derivative of f at x=c:

f’(c)=

Answer 0

lim (f(x) - f(c)) / (x-c)

x->c

Question 1

Limit definition of the derivative of f(x):

f’(x)=

Answer 1

lim (f(x+h) - f(x)) / (h)

h->0

Question 2

What f’(x) tells you about a function

Answer 2

• Slope of curve at a point
• Slope of tangent line
• Instantaneous rate of change

Question 3

Average rate of change

Answer 3

delta y         (f(b) - f(a))
———   =   —————
delta x            (b-a)