Find the value of c such that the line y=1/6x+3/2 is tangent to the curve y=(c)sqrt(x)

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nathanshields | High School Teacher | (Level 1) Associate Educator

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Tangent means the functions pass through the same point and have the same slope at that point.

So the derivatives must be equal:


And the y-values must also be equal (since the graphs pass through the same point):


So we have a system of two equations in two variables.  Let's solve each for c and then set them equal.



Setting these equal we have






x = 9 so c = 1.

Let's double-check that x/6+3/2 and sqrt(x) are tangent at the point (9,3):







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