Optimization Examples - Part 3: Minimizing Distance

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Optimization Examples - Part 3: Minimizing Distance
https://youtu.be/flBJsLXjUHk

In this video I use the calculus methods for curve sketching that I showed in my earlier videos and solve a very useful example on minimizing the distance between a point on a parabola and any given point.

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Download video notes: https://1drv.ms/b/s!As32ynv0LoaIiahywKANwgxKG87Njg?e=peFA6q

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# Optimization Examples – Part 3: Minimizing Distance

![Optimization Examples - Part 3.jpg](https://files.peakd.com/file/peakd-hive/mes/Ep3kB3mUaVDhdYyXH31ukrvZSG9a2r245hG88B2PG8vSbtRKfRNJjMVa2dmJFmhBy4S.jpg)

## Example 3

Find the point on the parabola y<sup>2</sup> = 2x that is closest to the point (1, 4).

### Solution

![image.png](https://files.peakd.com/file/peakd-hive/mes/Eo2BTut2ptshFxbBg8j1nowSfYtG2zhkPbzX48cbNafiD9jANb5KyDwdST27AEx1p8s.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9ym7bkpfoTNSswaWmPQcNq4jVR3vsg3byTQ2N3A8eXj4KrQvMkV23t33rnWQyt4.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/Eo4Js77WvPe4sUkuARrC96dB7X1qvhP6BmtyjLyfHWiKniBPaSCsDy6sxzidmRhPwNT.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8CfKPvxwq4Z7zp948dRzWkgryw1rT7NLgJEa82yEyb2t8T1dji2Gn4uuM8UahZ48vm.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHdQDGmsmd2Nr69XMgFsv38pbYSwhxjLmyfH6bpCPZD1rCPv7Wy6hzpbqByVmSdgjL8.png)
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