chapter 3 (intro to deivatives)

Question 1

average rate of change in t [a, x]

Answer 1

msec=f(x)-f(a)/x-a

Question 2

instantaneous rate of change [a, x] at a

Answer 2

m tan=lim(to a) f(x)-f(a)/x-a

Question 3

derivative definition xh

Answer 3

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

Question 4

if f is diferentiable at a then f is also

Answer 4

continuous at a

Question 5

when is f not differentiable

Answer 5

1. when it is not continuous
2. when there is a corner
3. when there is a vertical tangent line

Question 6

f’ c cis any real number

Answer 6

0

Question 7

f’n^x

Answer 7

xn^(x-1)

Question 8

f’ dx d is any constant

Answer 8

d(f’x)`

Question 9

f’(x+y)

Answer 9

f’x+f’y

Question 10

f’e^x

Answer 10

e^x

Question 11

f’(xy)

Answer 11

(f’x)y+x(f’y)

Question 12

f(x/g)

Answer 12

(g(f’x)-x(f’g))/g^2

Question 13

f’e^kx

Answer 13

ke^kx

Question 14

sin trig limit

Answer 14

lim (x-0) sinx/x=1

Question 15

cos trig limit

Answer 15

lim x-0 (cosx-1)/x=0

Question 16

average cost of production

Answer 16

c(x) (cost function)/x

Question 17

marginal cost

Answer 17

c’x

Question 18

elasticity D=f(p)

Answer 18

f’p*(p/d)

Question 19

f’ln x

Answer 19

1/x

Question 20

f’ b^x

Answer 20

b^xlnb

Question 21

f’ log(base B) x

Answer 21

1/(xlnb)

Question 22

explain how to do a related rates problem

Answer 22

1. read problem and then draw
2. write one or more equations that express the variable relationships
3. introduce rates of change by differentiating by t
4. substitute known values and solve for the known quantities