Given the functions $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 1$ and $g ( x ) = 6 x$, it is requested:\ a) (0.5 points) Justify, using the appropriate theorem, that there exists some point in the interval [1,10] where both functions take the same value.\ b) (1 point) Calculate the equation of the tangent line to the curve $y = f ( x )$ with minimum slope.\ c) (1 point) Calculate $\int _ { 1 } ^ { 2 } \frac { f ( x ) } { g ( x ) } d x$