15)

To solve this problem, it is first necessary to determine what it is asking. I can tell that the equation given is a position function because it talks about WHERE the object moves (“along the curve”). Looking at the second sentence, I see that I need to find the acceleration equation. Acceleration is the second derivative of a position equation, so I can use the power rule to find the second derivative. Finally, I can plug 7 seconds into my derived equation and solve for y’’.

Moving object (and its path)

17)

First draw a picture of the question; draw the person and the balloon, and how the numbers in the problem describe their relationship (or, how they RELATE).

Make sure you take the derivative of the formula with respect to x!!! *Pythagorean theorem is very helpful for this particular problem.

b=500 yd.db/dt=0

a=

200 y

d.

da/d

t=15 y

d./s

.

21)

Relative extrema are some or all of the critical value(s) found by setting the first derivative equal to 0. So do that and then test the critical values on a number line to make sure they mark a change in slope.

Relative maximums

FLASHCARDS

V’(t)

Hint: NOT

Change in velocity with respect to time; a.k.a. acceleration

S’(t)

Change in position with respect to time; a.k.a. velocity

Related Rates

Related rates occur when between RELATED variables, at least one is changing (aka a rate). The related rate is the rate of change between the variables.

They’re all RELATED!!!!Barack

Obama

Local Maximum

Local Minimum

FENCE (particularly a garden fence), BALLOON (volume)

Optimization

An optimist

BALLOON (rising), ROCKET, LADDER

Related Rates

Cone

•DEPENDENT variables: means it is necessary to set up a proportion

depends