Find the value of c such that the given line is tangent to the given curve?

Line: y = (3/2)x + 6


Curve: y = c(sqrt)x





I know this will involve deriving some of the equations, but how would I go about getting c?

Find the value of c such that the given line is tangent to the given curve?
Gradient of line is 3/2


Gradient of curve is c / (2√x).


So we need c / (2√x) = 3/2, i.e. c = 3√x.


We also need the line and curve to intersect at that point, so we need


(3/2)x + 6 = c√x


Substituting in c = 3√x gives us


(3/2)x + 6 = 3x


whence x = 4. Then c = 3√4 = 6.