Question: Find the point on the curve y=e^2x+1 where the tangent is parallel to the line y=2ex.
Please help. Thanks.
The graph of $\displaystyle y = e^2x+1$ is a straight line, so a tangent to it is itself. Since the slope of $\displaystyle y = e^2x+1$, which is $\displaystyle e^2$, is different from the slope of $\displaystyle y = 2ex$, which is $\displaystyle 2e$, no tangent to $\displaystyle y = e^2x+1$ is parallel to $\displaystyle y = 2ex$.
You set y' = 2e^(2x+1) = 2e and solve for x. The slope of the other curve, y=2ex, is 2e. So x=0, right?
All three of us were confused about what the function was; you really should have cleared that up in addition to asking for clarification.
- Hollywood