# How do you find the point on the curve #y=2x^2# closest to (2,1)?

##### 1 Answer

See the explanation.

#### Explanation:

Every point on the curve has the form:

The closest point is the one whose distance is minimum.

The distance between

Because the square root is an increasing function, we can minimize the distance by minimizing:

To minimize

Now use whatever tools you have available to solve this cubic equation. (Formula, graphing technology, successive approximation, whatever you have.)

The critical number is approximately

Clearly

The minimum value of distance occurs at

The closest point is about