Calculus questions...PLEASE HELP...?

Question

Okay, we are going over application of derivatives in class right now...I missed the lecture and am trying to understand this stuff the best I can off some notes that I borrowed...It's all about extrema...

1. The veolocity of a particle is (ft/s) is given by v=t^2 -7t +9, where t is time for which it has traveled.Find the time at which the velocity is at a minimum...
(I got the answer 3.5 s. Please correct if wrong...)

2. Find the absolute extreme values of each f(x).
f(x)= cscx [-pi/2 , 3pi/2]
(Would a max. and min. even exist?...This one really confuses me...Please help if you can...)

And lastly
3. Find the derivative at each critical point and determine the local extreme values...
(I don't really understand what this one is asking...)

PLEASE HELP IF YOU CAN...

Answer 1

v`(t)=2t-7=0 when t=3.5 so you are right
f`(x)=-sec(x)*cot(x) set this equal to zero and solve. Since this is the same as -cos(x)/sin^2(x)=0. The zero's occur when cos(x)=0: x=pi/2, 3pi/2, -pi/2.
To figure out whether these are maximum or minimum you could compute the second derivative and plug in the previous values; if the value is negative then you have a local maximum; if the value is positive then what you have is a relative minimum.

Answer 2

WHOA! Is that what you guys take in high school!? thats so hard!