Question 119
Let
$$
f(x) = \ln x \quad \text{and} \quad g(x) = \frac{1}{3} x^{3} - x^{2} - 6x + 4
$$
and let $p$ be the tangent to the graph of the function $f$ at the point $S(a, b)$, and $q$ the tangent to the graph of the function $g$ at the point $T(a, c)$. The tangent $p$ is perpendicular to the tangent $q$. Calculate the value of $a$.
$$
f(x) = \ln x \quad \text{and} \quad g(x) = \frac{1}{3} x^{3} - x^{2} - 6x + 4
$$
and let $p$ be the tangent to the graph of the function $f$ at the point $S(a, b)$, and $q$ the tangent to the graph of the function $g$ at the point $T(a, c)$. The tangent $p$ is perpendicular to the tangent $q$. Calculate the value of $a$.