D(x) doesn't represent the distance - it's the square of the distance. As it turns out, though, mininimizing the distance is equivalent to minimizing the square of the distance.chapsticks said:Homework Statement
Find the point on the graph of f(x)=√x that is closest to the value (4,0).
(differentiate the square of the distance from a point (x,√x) on the graph of f to the point (4,0).)
Homework Equations
f(x)=√x
The Attempt at a Solution
Square of distance from (4,0)
D(x)= ((x-4)^2+x)
This is the correct value of x, but you haven't answered the question, which is to find the point on the graph of f(x)=√x that is closest to the [STRIKE]value[/STRIKE] point (4,0).chapsticks said:For minimum, D'(x)=0
2(x-4)+1=0
x=7/2
The square of the distance is a mathematical concept that involves squaring the distance between two points. It is calculated by multiplying the distance by itself.
To differentiate the square of the distance, you need to use the power rule in calculus. First, square the distance and then differentiate it as you would with any other function. This will give you the derivative of the square of the distance.
Differentiating the square of the distance can help in solving problems related to motion, such as finding the velocity or acceleration of an object. It is also useful in calculating the slope of a line or the curvature of a curve.
No, the square of the distance and the distance squared are not the same. The square of the distance refers to the distance between two points being multiplied by itself, while the distance squared refers to the distance being multiplied by itself twice.
No, the square of the distance cannot be negative. Distance is a positive quantity and when squared, it will always result in a positive value. This is because the square of any number is always positive, regardless of the sign of the original number.