calculus problem

Question

The weight of a great white shark, W pounds, is given approximately by W=0.6x^3, where x is the length of the shark in feet. Suppose that a baby shark is growing at the rate of dx/dt= 0.4 ft/day

 

a.) How heavy is the shark when it's 2 ft long?

 

b.) At what rate is it gaining weight (pounds per dat) when it is 2 feet long? 10 feet long?

Answer 1

a) W = 0.6*2^3 = 0.6*8 = 4.8

 

 

b)   dW/dt = 3*0.6*x^2 *dx/dt

 

               x = 2 --->  3 ( 0.6)*2^2 * (0.4) = 2.88

 

                x=10 --->  3(0.6)*10^2 * (0.4) = 72