To find: The minimum distance such that the curve
![Check Mark](/static/check-mark.png)
Answer to Problem 41E
: The minimum distance is
Explanation of Solution
Given information: The equation of the curve
Formula used:
Distance d between two points
The minimum value of the function or the closest distance will be at the critical point of that function.
Calculation:
Determine the distance between the points
Square on both sides of the obtained equation and simplify the resulting equation.
Differentiate the obtained equation on both sides with respect to x.
Equate the obtained derivative to zero to get the critical point.
Now, determine the second derivative of the obtained distance by differentiating the obtained first derivative.
Since it is evident that the second derivative is positive or greater than zero at x=1, the distance between the given points will be minimum at x=1.
Determine the minimum distance by substituting 1 for x into the obtained distance function.
Substitute
As a result, the curve would come to close the point (3/2, 0) at a distance of
Chapter 4 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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