009B Sample Midterm 3, Problem 3 Detailed Solution

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Find a curve    with the following properties:


(ii)   Its graph passes through the point    and has a horizontal tangent there.

Background Information:  

1. If the graph of    passes through the point    then  

2. If    has a horizontal tangent at the point    then  


Step 1:  
Since    passes through the point   
Since    has a horizontal tangent at   
Step 2:  
Now, we have


Since    we have


Step 3:  
We have


Since    we have



Final Answer:  

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