To find the rate of change in profit when x=20 recorders are produced, we need to calculate the derivative of the profit function with respect to x and evaluate it at x=20. The derivative of the profit function P(x) = p * x - 60 * x is dP/dx = p - 60. Evaluating the derivative at x=20, we get dP/dx = p - 60. Therefore, the rate of change in profit when x=20 recorders are produced is p - 60. If the rate of change is positive (p > 60), the profit is increasing at this level of production. If the rate of change is negative (p < 60), the profit is decreasing at this level of production. If the rate of change is zero (p = 60), the profit is neither increasing nor decreasing at this level of production