chapter 3 (intro to deivatives) Flashcards
1
Q
average rate of change in t [a, x]
A
msec=f(x)-f(a)/x-a
2
Q
instantaneous rate of change [a, x] at a
A
m tan=lim(to a) f(x)-f(a)/x-a
3
Q
derivative definition xh
A
(f(x+h)-f(x))/h
4
Q
if f is diferentiable at a then f is also
A
continuous at a
5
Q
when is f not differentiable
A
- when it is not continuous
- when there is a corner
- when there is a vertical tangent line
6
Q
f’ c cis any real number
A
0
7
Q
f’n^x
A
xn^(x-1)
8
Q
f’ dx d is any constant
A
d(f’x)`
9
Q
f’(x+y)
A
f’x+f’y
10
Q
f’e^x
A
e^x
11
Q
f’(xy)
A
(f’x)y+x(f’y)
12
Q
f(x/g)
A
(g(f’x)-x(f’g))/g^2
13
Q
f’e^kx
A
ke^kx
14
Q
sin trig limit
A
lim (x-0) sinx/x=1
15
Q
cos trig limit
A
lim x-0 (cosx-1)/x=0
16
Q
average cost of production
A
c(x) (cost function)/x
17
Q
marginal cost
A
c’x
18
Q
elasticity D=f(p)
A
f’p*(p/d)
19
Q
f’ln x
A
1/x
20
Q
f’ b^x
A
b^xlnb
21
Q
f’ log(base B) x
A
1/(xlnb)
22
Q
explain how to do a related rates problem
A
- read problem and then draw
- write one or more equations that express the variable relationships
- introduce rates of change by differentiating by t
- substitute known values and solve for the known quantities
