The revenue (in dollars) from the sale of \( x \) units of a certain product can be described by \[ R(x)=100 x-0.01 x^{2} \text {. } \] Find the instantaneous rate of change of the marginal revenue.

We are given the revenue function: \[ R(x)=100x-0.01x^2. \] **Step 1. Find the Marginal Revenue** The marginal revenue is the derivative of the revenue function, \( R'(x) \). Differentiate \( R(x) \) with respect to \( x \): \[ R'(x)=\frac{d}{dx}(100x-0.01x^2)=100-0.02x. \] **Step 2. Find the Instantaneous Rate of Change of the Marginal Revenue** We now find the derivative of the marginal revenue, i.e., the derivative of \( R'(x) \). Differentiate \( R'(x)=100-0.02x \) with respect to \( x \): \[ R''(x)=\frac{d}{dx}(100-0.02x)=-0.02. \] The result \( -0.02 \) is constant, meaning that the instantaneous rate of change of the marginal revenue is \(-0.02\) dollars per unit.