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The differentiable function f measures the rate at which the temperature of a turkey in an oven is changing, in degrees Fahrenheit per hour, where t is measured in hours. What are the units of f^(')(t) ? degrees Fahrenheit degrees Fahrenheit / hour degrees Fahrenheit / hour ^(2) hours hours / degree Fahrenheit hours / degree Fahrenheit ^(2)

The differentiable function f f measures the rate at which the temperature of a turkey in an oven is changing, in degrees Fahrenheit per hour, where t t is measured in hours. What are the units of f′(t) f^{\prime}(t) ?\newlinedegrees Fahrenheit\newlinedegrees Fahrenheit / hour\newlinedegrees Fahrenheit / hour 2 ^{2} \newlinehours\newlinehours / degree Fahrenheit\newlinehours / degree Fahrenheit 2 { }^{2}

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Q. The differentiable function f f measures the rate at which the temperature of a turkey in an oven is changing, in degrees Fahrenheit per hour, where t t is measured in hours. What are the units of f′(t) f^{\prime}(t) ?\newlinedegrees Fahrenheit\newlinedegrees Fahrenheit / hour\newlinedegrees Fahrenheit / hour 2 ^{2} \newlinehours\newlinehours / degree Fahrenheit\newlinehours / degree Fahrenheit 2 { }^{2}
  1. Identify units: Identify the units of the given function f(t)f(t). The function f(t)f(t) measures the rate at which the temperature of a turkey is changing, in degrees Fahrenheit per hour.
  2. Understand derivative meaning: Understand the meaning of the derivative f′(t)f'(t). The derivative f′(t)f'(t) represents the rate of change of the rate of change of temperature, which is the second derivative of temperature with respect to time.
  3. Determine derivative units: Determine the units of f′(t)f'(t).\newlineSince f(t)f(t) has units of degrees Fahrenheit per hour, the derivative f′(t)f'(t) will have units of the rate of change of that rate. This means we take the units of f(t)f(t) and divide by the units of time once more, which is hours.
  4. Calculate derivative units: Calculate the units of f′(t)f'(t). The units of f′(t)f'(t) are (degrees Fahrenheit per hour) per hour, which can be written as degrees Fahrenheit per hour squared.

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