Consider the following function, where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars).
$R = -\frac{7}{9}x^3 + 7x^2 + 1$, $0 \le x \le 7$
Find $R'(x)$ and $R''(x)$.
$R'(x) = $
$R''(x) = $
Find the point of diminishing returns for the function, where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars). Use a graphing utility to verify your results.
$(x, R) = ($
