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