Week 10: group work by Ivan Limonchenko

2020-11-24 23:01:04 UTC

ilimonch — 2020-11-24 23:09:07 UTC

ilimonch — 2020-11-24 23:09:29 UTC

ilimonch — 2020-11-24 23:09:48 UTC

ilimonch — 2020-11-24 23:10:11 UTC

ilimonch — 2020-11-24 23:10:36 UTC

ilimonch — 2020-11-24 23:10:53 UTC

Room7

2020-11-25 20:50:21 UTC

a) f'(x) = 3x^2 -a =0

Room 3

2020-11-25 20:50:42 UTC

a)F'(x)=3x^2-a=0
x=+-root a/3

2020-11-25 20:51:49 UTC

(a/3)^0.5

Room 15

2020-11-25 20:56:04 UTC

if you find derivative of function and solve using quadratic formula you get x = sqrt(3a)/3 which means that there should be 2 different critical pts

2020-11-25 20:56:21 UTC

If a is positive

2020-11-25 20:56:36 UTC

Trying to find Dr/dt(speed of the beam).

when the point is 3km, the beam is moving at 4 revolutions/min is given and we are trying to find the speed of the beam at when the point is 1km away

2020-11-25 20:56:49 UTC

If a is zero

2020-11-25 20:57:16 UTC

If a is negative

2020-11-25 20:57:19 UTC

Room 3

2020-11-25 20:58:09 UTC

b) value of b do not matter, a<0, no critical point

2020-11-25 20:58:15 UTC

if a is zero; b doesn't matter; neither

2020-11-25 20:58:24 UTC

We want to find the instantaneous rate of change 1km from point p, we know

Room 3

2020-11-25 20:58:26 UTC

c)value of b do not matter, a=0, one critical point

2020-11-25 20:58:34 UTC

a < 0, b doesn't matter

2020-11-25 20:59:00 UTC

Highlight variables and important key words such as decreasing, increasing, speed, etc.

Room 3

2020-11-25 20:59:04 UTC

d) value of b do not matter, a>0, two critical points, the value of critical point change as value of a change.

Room7

2020-11-25 20:59:29 UTC

b) for a < 0 and b of all values, f(x) has no critical point.

room 7

2020-11-25 21:00:01 UTC

c) for a = 0 and b of all values, f(x) has one critical point and that is x = 0. This is neither a local maximum or local minimum.

Room 11

2020-11-25 21:00:12 UTC

Critical points:
x = + or - (a/3)^0.5

room 7

2020-11-25 21:00:32 UTC

d) for a > 0 and b of all values, f(x) has two critical points and that is x equals negative or positive root a/3. Point x = - (a/3)^1/2 gives the local maximum, while point x = (a/3) ^1 /2 gives the local minimum.

2020-11-25 21:02:19 UTC

a > 0, b doesn't matter