Please answer the question providing all steps and clear writing so I can understand. Thanks.You can see as a Reference book "James Stewart Calculus 8th Edition" to see similar solutions ### Problem 10Find the point on the curve \( y = \sqrt{2x} \) which is closest to the point \( (3,0) \).---To solve this problem, we can use the concept of minimizing the distance between a point on the curve and a fixed point. Let’s break down the solution for easier understanding.1. **Expression for Distance:** The distance \( D \) between any point \( (x, \sqrt{2x}) \) on the curve \( y = \sqrt{2x} \) and the point \( (3,0) \) can be given by the distance formula: \[ D = \sqrt{(x - 3)^2 + (\sqrt{2x} - 0)^2} \] Simplify the expression for \( D \): \[ D = \sqrt{(x - 3)^2 + 2x} \]2. **Minimizing the Distance:** To minimize the distance, we should minimize \( D^2 \) instead of \( D \) (since the square root function is monotonically increasing, the value that minimizes \( D^2 \) will also minimize \( D \)): \[ D^2 = (x - 3)^2 + 2x \] Let: \[ f(x) = (x - 3)^2 + 2x \] To find the minimum value of \( f(x) \), we take the derivative \( f'(x) \) and set it to zero: \[ f'(x) = 2(x - 3) + 2 \] \[ f'(x) = 2x - 6 + 2 \] \[ f'(x) = 2x - 4 \] Setting the derivative to zero to find the critical points: \[ 2x - 4 = 0 \] \[ 2x = 4 \] \[ x = 2 \]3. **Finding the Point on the Curve:** Substituting \( x = 2 \) back into the equation \( y = \sqrt{2x} \) to find the corresponding \(

Name: Please answer the question providing all steps and clear writing so I
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Description: Please answer the question providing all steps and clear writing so I can understand. Thanks.You can see as a Reference book "James Stewart Calculus 8th Edition" to see similar solutions ### Problem 10Find the point on the curve \( y = \sqrt{2x} \) w