week 8

Question 1

Critical number

Answer 1

number in f such that f’ is either zero or not defined. is local maxima or minima if it exists

Question 2

absolute maximum on closed interval

Answer 2

find critical points in interfal, evaluatre f for endpoints of interval. largest wins

Question 3

rolles theorem

Answer 3

there is a stationary point in a curve essentially.f needs to be equal at ends of interval, needs to be continuous on closed interval and differentiable on open interval.

Question 4

mean value theorem

Answer 4

there is some point in a differentiable curve such that the derivative is equal to the average rate of change.

Question 5

when f is increasing on interval

Answer 5

f’ is greater than zero

Question 6

if f’ changes sign on interval

Answer 6

there is a local maximum or minimum staitonary point

Question 7

concavity

Answer 7

rate of change of derivative. If a function is above tangent lines it is concavity up as gradient of lines is increasing so derivative is increasing

Question 8

inflection point

Answer 8

change of sign in concavity, when a curve stops getting steeper and starts getting shallower or vice versa

Question 9

a divides b

Answer 9

b = ac or b/a is an integer

Question 10

euclidean algorithm

Answer 10

last non zero remainder is hcf

Question 11

Fundamental theorem of algebra

Answer 11

n is a unique product of prime numbers

Question 12

proposition 11.5

Answer 12

if m divides n, then m has the same primes to diffirent powers up to the ones of n. for p2d2, any divisor is in pxdx where x goes up to 2

Question 13

lcm and hcf using prime expansion

Answer 13

the highest of the 2 for each prime gives lcm, lowest gives hcf