The cutlassfish is a valuable resource in the marine fishing industry in China. A von Bertalanffy model is fit to data for one species of this fish giving the length of the fish, L(a) (in mm), as a function of the age, a (in yr). An estimate of the length of this fish is L(a) = 612 – 400e-0.17a . Differentiate L(a) with respect to a, L'(a) = I mm/yr. Determine how fast the average fish is growing when it is 7 years old. L'(7) = H mm/yr.

Show that there are no points of the graph of y = log; x where the tangent line is horizontal.

The surface area of a human (in square meters) has been approximated by A = 0.024265h0.3964 m0.5378, where h is the height (in cm) and m is the mass (in kg). (a) Find the approximate change in surface area if the mass changes from 77 kg to 78 kg, while the height remains 182 cm. Use the derivative to estimate the change. (b) Find the approximate change in surface area when the height changes from 167 cm to 168 cm, while the mass remains at 75 kg. Use the derivative to estimate the change. (a) Differentiate A(m,h) with respect to m to find A(m,h). д Am(m,h): (0.024265h0.3964 m0.5378) = əm (Round to five decimal places as needed.) =

The population, P, of a mosquitoes colony at m month can be shown by a differentiation rule called the power rule: P (m) = 39x² + 10x – 9 A. What would be the initial population of the mosquitos colony? B. What is the population of the colony at m=6? C. What is the growth rate of the population at m=11?