Need help on this problem
have 0 idea what to do/how to start it...
In order for a line to be tangent to a curve, at a given point, both curve and line must pass through the point and must have the same derivative there.
So you need to find c and x such that $\displaystyle y= \frac{5}{6}x+ \frac{15}{2}= c\sqrt{x}$ and they have the same derivative for that x. That is two equations to solve for x and c.
I will give you one derivative free- the derivative of $\displaystyle y= \frac{5}{6}x+ \frac{15}{2}$ is $\displaystyle \frac{5}{6}$, for all x. What is the derivative of $\displaystyle c\sqrt{x}$? (That will depend on x.)