Question 1042791: Given the curve y=18/x
Find the value of m for which the line y=mx+12 is tangent to the curve and the co-ordinates of the point of contact.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! y = 18 / x
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we need the first derivative of this function, rewrite function as
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y = 18 * x^-1
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the first derivative, y' is determined by using the power rule
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y' = -18 * x^-2 = -18 / x^2
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we are given y = mx + 12
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The standard point slope form of a line
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y - y1 = m * (x - x1) and we want (x1, y1) a point on the line and the curve
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m = (-18 / x1^2)
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y1 = 18 / x1, from the function y = 18 / x
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y1 = (-18 / x1^2) * x1 + 12 from y = mx + 12, then
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12 = y1 + (18 / x1)
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12 = (18 / x1) + (18 / x1)
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x1 = 36 / 12 = 3
y1 = 18 / 3 = 6
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m = (-18 / 3^2) = -2
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equation of the tangent line at point (3,6)
y = -2x + 12
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