The function f(x)=x/(2x+1) -5 will decrease by approximately 0.6 as x decreases from 3 to 2.7. TRUE OR FALSE. How do I show the work. Not sure where to start.
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Just calculate the function when x = 3 and when x = 2.7. If f(3) is about .6 more than f(2.7), it's true
I don't need to do the derivitive of the problem?
The derivative is a rate of change; or how fast something is at a given point; how fast something is moving/changing. This question appears to be asking for a value of "how much" and not "how fast". But I could be mistaken...
So I agree with dwob...
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x is decreasing from 3 to 2.7. Would that not be a rate of change?
You technically could solve this with derivatives if you wanted to, but you'd find the derivative and then integrate it for no real reason. If I run and want to now how much weight I sweat off, I just weigh myself before and after. It's the same concept. Check the before (x = 3) and then check the after (x = 2.7) You don't need to know the speed that it sweat off (finding the derivative), just the total amount.
Thanks for the info. All of the other problems I have to do, deals with the derivative, so I just assumed this one would too.
The "slope" of the line at x=3 is -.2245
The "slope" of the line at x=2.7 = -.1997
So the slope of the line is increasing from 3 to 2.7 by .0252.
But, that is not a decrease in f(x); it is a decrease in the slope of the line that is tangent to the curve at f(x) Either way, I would say it is false.