SOLUTION: 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.

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
:
we need the first derivative of this function, rewrite function as
:
y = 18 * x^-1
:
the first derivative, y' is determined by using the power rule
:
y' = -18 * x^-2 = -18 / x^2
:
we are given y = mx + 12
:
The standard point slope form of a line
:
y - y1 = m * (x - x1) and we want (x1, y1) a point on the line and the curve
****************************************************************************
m = (-18 / x1^2)
:
y1 = 18 / x1, from the function y = 18 / x
:
y1 = (-18 / x1^2) * x1 + 12 from y = mx + 12, then
:
12 = y1 + (18 / x1)
:
12 = (18 / x1) + (18 / x1)
:
x1 = 36 / 12 = 3
y1 = 18 / 3 = 6
:
m = (-18 / 3^2) = -2
:
*******************************************
equation of the tangent line at point (3,6)
y = -2x + 12
*******************************************
:

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