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anonymous
 5 years ago
Suppose that we know that f(x) is a continuous and differentiable function on [2,14]. Also, suppose we know that f(2)=9 and f'(x) is greater than or equal to 12. What is the smallest possible value of f(14)?
anonymous
 5 years ago
Suppose that we know that f(x) is a continuous and differentiable function on [2,14]. Also, suppose we know that f(2)=9 and f'(x) is greater than or equal to 12. What is the smallest possible value of f(14)?

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0would this be a straight line from 2,14 running at a slope of 12?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(I'm supposed to use the mean value theorem, or at least that's what it says on the worksheet.)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(I'm supposed to use the mean value theorem, or at least that's what it says on the worksheet.)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0@amistre64  I have no idea! I'm complete lost on this one. Don't even know where to start.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f'(2) =>12....6x? maybe

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, if f'(x) = 12 throughout the interval then it would be a straight line from (2,9) with a slope of 12. So that would be the minimum possible value given what we know.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, @polpak  how do we know that?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ahh,....()12 ... that was hiding in the corner

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We are given that f'(x) is greater than or equal to 12.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So if it maintained the smallest possible derivative over the whole interval we would have a line with slope of 12.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i got the smallest possible value is 135 for f(14)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats what I thought :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0912*12 = 9144 = 135

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0yay thats what i got except differently

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.012<=[f(2)f(14)]/[214]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Does that make sense Chap?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0How do you figure what f(14) is?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0chap you can also solve the above for f(14) resulting in f(14)>=(135)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0I used the mean value thm just like you said

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right. But I have 12<= 9  f(14)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I have 12 <= 9  f(14)  12

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0multipliy 12 on both sides don't forget to flip the inequality when you multipliy or divide by a negative

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry )= I don't understand how to do that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[12 \le \frac{9 f(14)}{12} \implies 144 \ge 9f(14)\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0how do you solve x/5=4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[4a < b \implies a \gt \frac{b}{4}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay. But how does 135 >=  f(14) solve for f(14)?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0now multipliy both sides by negative 1 don't forget to flip

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0wait where's the negative?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0ok so we have f(14)>=135 this means the smallest that f(14) can be is 135

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0OH! I thought f(14) would be positive. Thank you so much!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It might be positive!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We only know that the smallest it can be is 135. It could be very very large.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0it could be 1111111111111111111111

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.05 trillion billion if that means anything
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