Respuesta :
The pulse rate of a person x inches tall is given by the function:
[tex]y=610x^{-\frac{1}{2}}[/tex]To find the instantaneous rate of change of the pulse rate, we need to find the first derivative of this function and then solve for the x inches tall given.
Follow the next steps:
1. Apply the constant multiple rule of derivatives:
[tex]y^{\prime}=610\frac{d}{dx}(x^{-\frac{1}{2}})[/tex]2. Now, to find the derivative apply the power rule of derivatives:
[tex]\begin{gathered} y^{\prime}=610\times-\frac{1}{2}x^{-\frac{1}{2}-1} \\ y^{\prime}=610\times-\frac{1}{2}x^{-\frac{3}{2}} \\ y^{\prime}=-\frac{610x^{-\frac{3}{2}}}{2} \\ y^{\prime}=-\frac{305}{x^{\frac{3}{2}}} \end{gathered}[/tex]a. A person 37 inches tall will have the following instantaneous rate of change of the pulse rate:
[tex]\begin{gathered} f^{\prime}(37)=-\frac{305}{37^{\frac{3}{2}}} \\ f^{\prime}(37)=-\frac{305}{225.1}^{} \\ f^{\prime}(37)=-1.36 \end{gathered}[/tex]b. A person 63 inches tall will have the following instantaneous rate of change of the pulse rate:
[tex]\begin{gathered} f^{\prime}(63)=-\frac{305}{63^{\frac{3}{2}}} \\ f^{\prime}(63)=-\frac{305}{500.05} \\ f^{\prime}(63)=-0.61 \end{gathered}[/tex]