(Solved): The growth of a red oak tree is approximated by the model \[ f(x)=-0.003 x^{3}+0.137 x^{2}+0.458 x- ...

The growth of a red oak tree is approximated by the model \[ f(x)=-0.003 x^{3}+0.137 x^{2}+0.458 x-0.839 \] where \( f(x) \) is the height of the tree in feet and \( x \) is its age in years where \( 0 \leq x \leq 50 \). Find the age of the tree when it reaches its tallest height (critical point) and find when it is growing. most rapidly. (inflection point). Round to the nearest year.