Hi. Someone can help me with this.
a) Discover in the grafic of the funcion the point with abscissa c knowing that the line that is tangent with c is parallel with the secant line that passes on the points with abscissa 1 and e.
b) Show that
Abscissa?. Why not just say x=c. Wonder why some texts insist on showing off with Rube Goldbergian jargon?.
If I am reading this correctly, it appears to be a problem related to the Mean Value Theroem.
To find the point c, which by the MVT should be between 1 and e:
Solve for c.
Here's the graph with the tangent line and the secant line. Note they are parallel as per the MVT.
You can now find the equation of your tangent line, if needed.