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Rough sketch of exponential graph without derivatives

  • Thread starter Batmaniac
  • Start date
1. The problem statement, all variables and given/known data

Roughly sketch e^x + x - 2 to show that it has only one root. This is given before we learn derivatives and the curve sketching algorithm, but after we have gone through limits and asymptotes.


3. The attempt at a solution

Well, the graph of e^x - 2,is easy enough, a simple exponential graph shifted down by 2. But what does the +x do to the graph from there? I've no idea. I could sketch it using the curve sketching algorithm we learned in high school calculus, but we don't cover that for another month or so in this course so I know it's expected to be done by other methods (mostly intuition!), especially since it's just a really rough sketch they want.

- thanks
 

rock.freak667

Homework Helper
6,230
31
Let [tex]y=x^2-3x+2[/tex] to find how many roots this eq'n has you would equate y to zero and solve right?
but what in fact you are really doing graphically is drawing the graph of the left side and the graph of the right side and finding where they intersect.

so for your situation
let [tex]y=e^x + x - 2=o[/tex] now there are many graphs you can draw to show that there is only one root.

you could put [itex]e^x + x=2[/itex] and draw the curve [itex]y=e^x + x[/itex] and the line [itex]y=2[/itex] and show that they intersect one point. Or you could draw [itex]y=e^x[/itex] and the line [itex]y=2-x[/itex] and so forth...So pick which ever combination you find easiest or most useful to draw
 
That's an awesome method for finding roots of complex functions. I never knew you could break them up like that.

Thanks a lot!
 

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