Calculus help request

I'm having a little difficulty with a calculus problem involving taking the derivative. This is college-level calculus. Is anyone able to help?

what's the question?

@johnnyz256: question?

@masterkungfu: I asked the question on Yahoo Answers before here and was responded to. I just didn't factor at the end, so I wasn't sure what had gone wrong. Thanks for replying, though.

@johnnyz256: do you have the link?

https://answers.yahoo.com/question/index?qid=20150414205441AASfovM

@johnnyz256: Check out Khanacademy on YouTube if you need any other help. It helped me get through calc.

I'm doing Trig right now

@masterkungfu: If you don't mind, I have another question. It concerns average velocity of a falling object.

The question states that the height of an object t seconds after it's dropped from a height of 300 meters is s(t) = -4.9t^2 +300.

In the first part, it wants to know average velocity during the first 3 seconds. So I did s(3) - s(0), and divided that by 3 (3-0). I got

(255.9 - 300) divided by 3, or -14.7 meters/second. Is this correct? I believe it is.

In the second part, though, I'm sort of confused. It says to use the Mean Value Theorem to verify that at some time during the first 3 seconds of fall, the instantaneous velocity equals the average velocity.

MVT says that instantaneous rate of change equals average rate of change over interval. In my question, the derivative of -4.9t^2 + 300, or just -9.8t, should equal -14.7. In the last part, it asks to find the time referred to in part B, which I think would be calculated by dividing 14.7 by 9.8, but I'm confused about part 2.

Thanks for any help that you can give.

@johnnyz256: sorry I couldn't reach you in time. I was reading through and working out your solution when my router was turned off. never mind who turned it off

anyways I can say for sure you got the first part right

for the second part I suggest using this formula

equate your previous equation below to f(c)

find the derivative of S with respect to t and you should get (at) since u = 0

note : this is your LHS of the formula

for your RHS it is the answer you got for the first part

therefore your final equation should be s'(c) = at = 9.8t = 14.7 where a = 9.8 for acceleration of gravity

you don't need to divide because s'(c) is your instantaneous velocity which is = 14.7m/s

for average velocity use the formula (velocity = displacement over time)

find displacement by substituting t=3, u=0, a=9.8 in the second formula on screen. you should get 44.1m

your time should be 3 seconds should divide 44.1 by 3 you should get 14.7m/s

therefore your inst veloc = av veloc

hope this helps

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