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??
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.
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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!