To find the point of diminishing returns for the given revenue function:

$R = -1.71 \left(x^3 - 12x^2 - 6\right)$

we need to locate the inflection point of this function, as the hint suggests. Inflection points occur where the second derivative changes sign, indicating a change in the concavity of the graph, which can signify the point where revenue growth starts to slow down (diminishing returns).

Step-by-Step Solution

1. First Derivative $R'(x)$: Find the first derivative $R'(x)$ to understand the rate of change of revenue with respect to $x$ (advertising).

   $R(x) = -1.71 \left(x^3 - 12x^2 - 6\right)$ Using the chain rule: $R'(x) = -1.71 \cdot (3x^2 - 24x)$ Simplifying: $R'(x) = -1.71 \cdot 3x^2 + 1.71 \cdot 24x$