Tangent to the curve

[Matt2007]

I was struggling with this question and wasn't sure how to exactly prove that it passes through the origin but I gave it a go and was wondering if my answer was correct or if there's a better way to answer it. Any help I would greatly appreciate and be very thankful

 

[skeeter]

tangent line equation at the point [imath](2,e)[/imath] ...

[math]y - e = \dfrac{e}{2}( x - 2)[/math]
[math]x = 0 \implies y = 0[/math]

 

[Dr.Peterson]

I was struggling with this question and wasn't sure how to exactly prove that it passes through the origin but I gave it a go and was wondering if my answer was correct or if there's a better way to answer it. Any help I would greatly appreciate and be very thankful
View attachment 28659View attachment 28660

You wrote an equation that necessarily passes through the origin, so verifying that it does proves nothing!



Did you notice that you never used the coordinates of the point of tangency?

 

[Matt2007]

tangent line equation at the point [imath](2,e)[/imath] ...

[math]y - e = \dfrac{e}{2}( x - 2)[/math]
[math]x = 0 \implies y = 0[/math]

thank you so much!!

 

[Matt2007]

You wrote an equation that necessarily passes through the origin, so verifying that it does proves nothing!

View attachment 28663

Did you notice that you never used the coordinates of the point of tangency?

Thank you so much!! I understand how to do it properly now