Final

Question 1

Derivative (a)`

Answer 1

lim= f(x)-f(a)/
x->a x-a

Question 2

Derivative (h)

Answer 2

lim= f(x+h)- f(x)/
h->0 h

Question 3

Chain Rule

Answer 3

f’(g(x))= f’(g(x)*g’(x)

Question 4

d/dx a^x

Answer 4

a^x*lna

Question 5

d/dx logb x

Answer 5

1/xlnb

Question 6

d/dx lnx

Answer 6

1/x

Question 7

d/dx e^x

Answer 7

e^x

Question 8

d/dx ex^x-1

Answer 8

ex^e-1

Question 9

blnx=

Answer 9

lnx^b

Question 10

lnx^b=

Answer 10

blnx

Question 11

ln(a*b)

Answer 11

lna+lnb

Question 12

ln(a/b)

Answer 12

lna-lnb

Question 13

Substrate velocity equation

Answer 13

V=Vmax[S]/Km + [S]
V= velocity
Km= [S] @ Vmax/2 (y)
[S]= substrate concentration (x)

Question 14

Growth/Decay Equation

Answer 14

P(t)= Ae^rt
A= initial
r=growth >0 , decay <0
t=time

Question 15

Rate of Growth/Decay

Answer 15

d/dx of Growth/Decay Function

Question 16

Habitat–> species (Logistic Function)

Answer 16

P(t)=A/1+Be^-kt
A=max pop.
B=# (use 0,z to solve)
k=growth or decay constant

Question 17

Logistic Function WHEN GROWING

Answer 17

d’

Question 18

Logistic Function when fastest

Answer 18

d’’

Question 19

Logistic Function INFLECTION VALUE

Answer 19

(t, A/2)

Question 20

How do you find critical numbers?

Answer 20

f’(x)

Question 21

How do you find relative max/min?

Answer 21

Test where d’(x) is >/<0 using critical numbers
+ –> - max
- –> + min

Question 22

How do you find the intervals of concavity?

Answer 22

Where d’’ =0
<0 concave downwards
>0 concave upwards

Question 23

How do you find the absolute maximum ?

Answer 23

Find critical points using 0=f’(x)
Plug critical & end points into f(x)
Greatest–> max
Least–> min