question_answer

The tangent to the curve \[y={{e}^{x}}\] drawn at the point \[(c,{{e}^{c}})\] intersects the line joining the points \[(c-1,{{e}^{c-1}})\] and \[(c+1,{{e}^{c+1}})\] is

A) on the left of \[x=c\]

B) on the right of c

C) at not point

D) at all points

Correct Answer: A

Solution :

Slope of line joining the points \[(c-1,{{e}^{c-1}})\]and \[(c+1,{{e}^{c+1}})\] is equal to \[\frac{{{e}^{c+1}}-{{e}^{c-1}}}{2}>{{e}^{c}}\]

\[\Rightarrow \]tangent to the curve \[y={{e}^{x}}\]will intersect the given line to the left of the line x = c.