Consider the function as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. R(t) = 50 + 70t - th; t = 5 Find the average rates of change of R(t) over the time intervals [t, t + h], where t is as indicated and h = 1, 0.1, and 0.01 days. (Use smaller values of h to check your estimates.) HINT [See Example 1.] h 0.1 0.01 Avg. Rate Estimate the instantaneous rate of change of R at time t, specifying the units of measurement. R'(5) = S/day The function gives the cost to manufacture x items. C(x) = 15,000 + 8x - - X = 15,000 20,000 Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated and h = 10 and 1. (Use smaller values of h to check your estimates. Round your answers to five decimal places.) 10 Cave Estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. C'(15,000) = | S/item v V The graph of a function is shown together with the tangent line at a point P. Estimate the derivative of f at the corresponding x-value. X The graph of a function is shown together with the tangent line at a point P. Estimate the derivative of f at the corresponding x-value. X