I am being asked to find a tangent line of the function ln(x) at the point where x=1.
MY understanding is that to do so I can set up the equation of the line using these formulas.
1) F ' (c)= (f(b)-F(a)) / (b-a)
2) then since f ' (x) = 1/x I can set this equal to answer in step 1)
3)Then I take the point and substitute and put it in to slope intercept form. This is all fine, but the problem comes in when I plug my x coordinate (1) into the original function and get that Y=0
so....... In step 1) I obviously cant calculate ln(0) because it doesn't exist. so does that mean that my slope will be 1 or is it possible to use differentials to find an approximate value for ln(0). I used differentials seeing as a slope of one will not give me the tangent line I am looking for. Using differentials I calculated that ln(0) is close to equal to -1. Using this, my slope became 2 and the line I got out of this was pretty close to being a tangent line at x=1. My question is whether or not this is a suitable answer or is there a better way of going about finding this tangent line. I just took my final exam and have been worrying about this. Any help would be appreciated.
MY understanding is that to do so I can set up the equation of the line using these formulas.
1) F ' (c)= (f(b)-F(a)) / (b-a)
2) then since f ' (x) = 1/x I can set this equal to answer in step 1)
3)Then I take the point and substitute and put it in to slope intercept form. This is all fine, but the problem comes in when I plug my x coordinate (1) into the original function and get that Y=0
so....... In step 1) I obviously cant calculate ln(0) because it doesn't exist. so does that mean that my slope will be 1 or is it possible to use differentials to find an approximate value for ln(0). I used differentials seeing as a slope of one will not give me the tangent line I am looking for. Using differentials I calculated that ln(0) is close to equal to -1. Using this, my slope became 2 and the line I got out of this was pretty close to being a tangent line at x=1. My question is whether or not this is a suitable answer or is there a better way of going about finding this tangent line. I just took my final exam and have been worrying about this. Any help would be appreciated.