I've tried so many different eqns but they all end up in tangent lines that pass through 2 points on the function very close to each other. Please help!

- Thread starter casherr
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I've tried so many different eqns but they all end up in tangent lines that pass through 2 points on the function very close to each other. Please help!

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your initial post says "one rational function" ... nothing about its complexity.it has to be somewhat complex, like x+3/x+2 for example

so, how about \(\displaystyle f(x) = \dfrac{4}{x^2+1}\) ?

does that meet the "somewhat complex" criteria?

If so, determine the unique value \(\displaystyle x=a \) where \(\displaystyle f'(a) = -2\)

Also, unrelated but if I were to find the instantaneous rate of change for one point on an income per person per year graph, what would my units be?

thank you for all your help so far by the way!

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You say:

Also, unrelated but if I were to find the instantaneous rate of change for one point on an income per person per year graph, what would my units be?

thank you for all your help so far by the way!

will there ever be a point on the graph with the slope -2 that only intersects once?

Are you referring to the graph - with slope -2 (i.e. the graph has a slope of -2 at some given point)?

You say - only intersects once →

will there ever be a point on the graph with the slope -2 that only intersects once?

Are you referring to the graph - with slope -2 (i.e. the graph has a slope of -2 at some given point)?

You say - only intersects once →whatintersects withwhat?

tangent line that only intersects with the graph once at a specific point with the slope -2

im referring to the graph we just discussed, y= 4/(x^2+1), and what point would have tangent -2 that's line only intersects with the graph once

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not with the function I proposed ... not saying it isn't possible with some other functionwill there ever be a point on the graph with the slope -2 that only intersects once?

(income per person) per year, or (income) per (person per year) ? there is a differenceAlso, unrelated but if I were to find the instantaneous rate of change for one point on an income per person per year graph, what would my units be?

I suspect you may mean the first ... if so, the derivative would be (income per person) per year

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then the slope would be (income per person) per year, \(\displaystyle m = \dfrac{\text{income/person}}{\text{year}}\)x is years

y is the income per person in dollars