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mg2
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Homework Statement
Find the point on the curve y=√(4x) that is closest the the point (3,0)
Homework Equations
The Attempt at a Solution
I don't even know where to start.
mg2 said:It wasnt given. The only thing given was the point, and the equation.
To find the point on the curve that is closest to the given point, you will need to use the distance formula and the derivative of the curve. First, set up the distance formula with the given point as one point and the point on the curve as the other point. Then, use calculus to find the derivative of the curve. Finally, set the derivative equal to zero and solve for x to find the x-coordinate of the closest point. Plug this x-coordinate back into the original equation to find the y-coordinate of the closest point.
The distance formula is a formula used to calculate the distance between two points on a coordinate plane. It is √[(x2-x1)² + (y2-y1)²], where (x1,y1) and (x2,y2) are the coordinates of the two points.
To find the derivative of a curve, you will need to use calculus. Specifically, you will need to use the power rule if the curve is in the form y = x^n. If the curve is not in this form, you will need to use other derivative rules such as the product rule or the chain rule.
Setting the derivative equal to zero allows you to find the critical points of the curve, which are the points where the slope of the curve is either flat (horizontal) or undefined (vertical). These points can help you identify local maximum or minimum points, which in this case, will be the point on the curve closest to the given point.
Yes, this method can be used for finding the closest point to a given point on any curve, as long as the curve is differentiable (has a derivative) at the point in question. However, the process may be more complex for curves that are not in the form y = x^n and may require the use of different derivative rules.