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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 14P

To determine

**To find:**The point on the highway will the car’s headlights illuminate the status.

Expert Solution

The point on the highway will the car’s headlights illuminate the status at

**Given information:**

The car travelling along a highway shaped like parabola with its vertex at the origin as shown in figure (1).

Figure (1)

**Calculation:**

The parabola has the vertex at

The point

So, the equation of parabola is.

Assume that the headlight of the car illuminates the statue at the point of coordinate

The coordinate of the statue is

Calculate the slope of the tangent line at any point is.

Theslope of the tangent line at

The equation of tangent line is.

It passes through the point

As we know that,

Substitute

The minus sign is the right one, and the other one corresponds to when the taillights of the car would be illuminating the statue.

The value of

Therefore, the point on the highway will the car’s headlights illuminate the status at