anonymous
  • anonymous
Help would be much appreciated ^.^ -Find the absolute and local maximum and minimum values of f(t) = 2/t + 10 , 0 < t ≤ 4
Mathematics
chestercat
  • chestercat
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myininaya
  • myininaya
Well we know we need to find f'(t) is f(t)=2/t+10 or f(t)=2/(t+10)?
anonymous
  • anonymous
the 1st one :)
myininaya
  • myininaya
just so i can know to check your derivative

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myininaya
  • myininaya
ok cool
myininaya
  • myininaya
\[f(t)=\frac{2}{t}+10 \\ f(t)=2t^{-1}+10 \\\] do you know how to find f'?
anonymous
  • anonymous
Yes! It's \[f'(t)= \frac{ -2 }{ t^2 }\] am I right?
myininaya
  • myininaya
yes and f' is not zero ever but f' dne at t=0 but we f(0) also doesn't exist at t=0 we actually have a vertical asymptote |dw:1434748364786:dw| so we don't have to worry about critical numbers but this just shows we also don't have any max of any type but w do have a min and it is an absolute min (you know since local min can't occur at endpoints)
myininaya
  • myininaya
so you just need to consider the endpoints of your interval given
myininaya
  • myininaya
tell me if you can find the absolute min?
anonymous
  • anonymous
Ohhh I understand. How can I find the absolute max. and min. ?
myininaya
  • myininaya
there is a vertical aysmptote in the pic and as x approaches it from the right the y values keep getting bigger and bigger there is no max you only need to find the absolute min and I gave you a big hint for that it occurs at the endpoint for this question
myininaya
  • myininaya
|dw:1434748634077:dw|
anonymous
  • anonymous
Oh yeah! So I plug in 4 into the original function and that will be my abs. min. ?
myininaya
  • myininaya
yes
anonymous
  • anonymous
So that means it is 10.5 ?
myininaya
  • myininaya
yes
myininaya
  • myininaya
no calculus was actually needed on this problem
anonymous
  • anonymous
If I did not known what the graph looked like would I still be able to find it?
myininaya
  • myininaya
Yes.
myininaya
  • myininaya
I said no calculus was needed because g(x)=1/x is a pretty basic graph learned in algebra. f(x)=2/x+10 is just a translation of that graph. Anyways f(x)=2/x+10 , 0
anonymous
  • anonymous
@myininaya thank you so much!!!
myininaya
  • myininaya
Means there is no abs max at all.* Since there were no critical numbers then there are no relative max/min

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