Find the equation of the tangent to the curve with equation

$$y=\frac{1}{6}{x}^3-9x^{\frac{1}{2}}$$

at the point $P(9,94.5)$.

Give your answer in the form $ax+by+c=0$, where $a$, $b$ and $c$ are integers.

The curve with equation $y=f(x)$ also passes through the point $P(9,94.5)$. Given that

$$f^{\prime }(x)=\frac{1}{6}{x}^3-9x^{\frac{1}{2}}$$

find $f(x)$, giving the coefficients in simplest form.