\f2x x2+1 Find an equation of the tangent line to the graph of y= at the origin and at the point ( - 1,- 1). The tangent to the curve at the origin is y = D. An accessories company nds that the cost, in dollars, of producing x belts is given by C(x) = 790 + 32x - 0.063x2. Find the rate at which average cost is changing when 174 belts have been produced. First, find the rate at which the average cost is changing when x belts have been produced. / C (X) = 9 An accessories company nds that the revenue, in dollars, from the sale ofx belts is given by R(x) = 25x10 . Find the rate at which average revenue is changing when 172 belts have been produced and sold. First, find the rate at which the average revenue is changing when x belts have been produced. 9 An accessories company nds that the cost and revenue, in dollars, of producing x belts is given by C(x) = 740 +40x - 0.065x2 and R(x) = 55x10 , respectively. Determine the rate at which the accessories company's average profit per belt is changing when 175 belts have been produced and sold. First, find the rate at which the average prot is changing when x belts have been produced. P'(x) = The population P, in thousands, of a small city is given by the following function, where t is time in a) Find the growth rate. years. Answer parts a) through c). The growth rate is 500t P(t) = 312 + 4 80. AP + 70- 60- 50- 40- 30- 20- 10- 5 6 7 8 9 10 11 1210t t2+2 (a) Find the rate of change of the temperature with respect to time. (b) Find the temperature at t= 1 hr. (0) Find the rate of change of the temperature at t=1 hr. The temperature T of a person during an illness is given by T(t) = AT(t) + 98.6, where T is the temperature, in degrees Fahrenheit, at time t, in hours. 104 98 1O (a) Find the rate of change of the temperature with respect to time. T'(t) =