Question

The time that a turkey cooks is measured by y minutes for x pounds and is given by the function y = f(x). What are the units of:

A) f′(10)
B) f''(10)

Answer 1

The units of f'(10) are minutes per pound, representing the rate at which the cooking time per pound changes with respect to the weight of the turkey. The units of f''(10) are minutes per pound squared, representing the rate at which the rate of change of the cooking time per pound changes with respect to the weight of the turkey.

Step-by-step explanation:

The units of f'(10) are minutes per pound. To find f'(10), we need to take the derivative of the function y = f(x) with respect to x. In this case, the derivative represents the rate at which the cooking time per pound is changing with respect to the weight of the turkey. So, f'(10) tells us how many minutes the cooking time changes for each additional pound of turkey when the weight is 10 pounds.

The units of f''(10) are minutes per pound squared. To find f''(10), we need to take the second derivative of the function y = f(x) with respect to x. In this case, the second derivative represents the rate at which the cooking time per pound is changing with respect to the weight of the turkey. So, f''(10) tells us how the rate of change of the cooking time per pound is changing with respect to the weight of the turkey at a weight of 10 pounds.