How to find the equation of the curve and the x-coordinate? PLEASE HELP, 10 POINTS
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How to find the equation of the curve and the x-coordinate? PLEASE HELP, 10 POINTS

[From: ] [author: ] [Date: 12-04-25] [Hit: ]
Since (3/2)/√4 = 3/4 is positive, the stationary point is a relative minimum.Smile! You will get it one day!......
A curve is such that dy/dx = 3x^(1/2) - 6 and the point (9,2) lies on the curve. Find the equation of the curve, then find the x-coordinate of the stationary point on the curve and determine the nature of the stationary point.
Please help me solve this problem, 10 points??

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The indefinite integral is 2x^(3/2) - 6x + C. Using the point (9, 2),
2 = 2(√9)³ - 54 + C
2 = 54 - 54 + C [or -54 - 54 + C]
C = 2 [or 110]

The curve is y = 2x^(3/2) - 6x + 2

The stationary point is where 3√x - 6 = 0, or √x = 2, x = 4.
Since (3/2)/√4 = 3/4 is positive, the stationary point is a relative minimum.

Smile! You will get it one day!
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