Part 2 of 2 \( y=597 x^{-1 / 3} \) for \( 30 \leq x \leq 75 \). What is the instantaneous rate of change of pulse rate for the following heights? (A) 40 -inches (B) 61 -inches beats per minute, as given approximately by What is the instantaneous rate of change of pulse rate for a 40 inch tall person? -1.45 beats per minute per inch (Round to the nearest hundredth as needed.) What is the instantaneous rate of change of pulse rate for a 61 inch tall person? \( \square \) beats per minute per inch (Round to the nearest hundredth as needed.)

To find the instantaneous rate of change of pulse rate for a height of 61 inches, we need to find the derivative of the function \( y = 597 x^{-1/3} \) and then evaluate it at \( x = 61 \). First, we differentiate \( y \): \[ \frac{dy}{dx} = 597 \cdot \left(-\frac{1}{3} x^{-4/3}\right) = -199 x^{-4/3} \] Next, we plug in \( x = 61 \): \[ \frac{dy}{dx}\bigg|_{x=61} = -199 \cdot 61^{-4/3} \] Now, calculating \( 61^{-4/3} \): \[ 61^{-4/3} = \frac{1}{(61^{1/3})^4} \approx \frac{1}{(3.936)^4} \approx \frac{1}{246.643} \approx 0.00405 \] Now substituting back: \[ \frac{dy}{dx}\bigg|_{x=61} \approx -199 \cdot 0.00405 \approx -0.80495 \] Rounding to the nearest hundredth, we get: \[ \frac{dy}{dx}\bigg|_{x=61} \approx -0.80 \text{ beats per minute per inch.} \] So, the instantaneous rate of change of pulse rate for a 61-inch tall person is approximately -0.80 beats per minute per inch.