For what values and is the line tangent to the curve at the point with ?
(A) Use the limit process, as we did in class, to find the slope of the tangent line to when . (Your answer will contain an .)
The slope of the tangent line to when is .
(B) What is the slope of the line ?
The slope of this line is .
(C) In order for the line to be tangent to the curve at , we need for the slope of the tangent line to at to be the same as the slope of the line .
Thus in comparing (A) and (B), we find that
(D) Lastly, in order for the line to be tangent to the curve at , the graphs of and must have the same -coordinate at .
Comparing the -coordinates of the two graphs tells us that
You can earn partial credit on this problem.