unit 04

Question 1

mean value theorem

Answer 1

make f(x), f(c) (replace x with c) and find f prime of c
then use a and b from interval and plug into f using f(b)-f(a) / b-a
set f prime of c to the number and solve for c

Question 2

motion application

Answer 2

velocity is v prime
acceleration is double prime

when a and v are same sign its speeding up

Question 3

proof problems

Answer 3

d2y/dx2 = d/dx (dy/dx)
plug into dy/dx with equation given and solve derivative
multiply by y’ because implicit
plug into y’ and simplify to match equation

Question 4

for questions like…

foes g have a relative man, minimum, or neither at x=#

do..

Answer 4

dy/dx |x,y and plug into that equation

dy/dx |x,y and plug into double prime equation

if less than 0, negative, concave down and rel max - vice versa

Question 5

for finding absolute max and minimum in a stated interval

Answer 5

find derivative of equation then set equal to 0 and find what x =
if isnt between interval ignore
make a chart if x and f(x)
x is the sides of interval and number gained from derivative=0, plug number in an find max and min

Question 6

f, f’, f’’ chart

Answer 6

f | f’ | f’’
inc |+ |
dec | - |
rel ext| sign change |
conc up | inc | +
conc dn | dec | -
POI | rel ext | sign change

Question 7

unit circle

Answer 7

pi/2 , pi/3 , pi/4 , pi/6 , 0

(0,1), (1/2, sqrt3/2), (sqrt2/2, sqrt2/2), (sqrt3/2, 1/2), (1,0)