# Rate of change problem involving pulse rate

The average pulse rate $y$ (in beats/minute) of a healthy person $x$ inches tall is given approximately by the formula:

$$y = \frac{590}{\sqrt x}\quad 30 \leq x \leq 75$$

Approximately how will the pulse rate change for a change in height from $36$ to $37$ inches and $64$ to $65$ inches?

The first step I took was to differentiate $y$, which is

$$\frac{dy}{dx} = -\frac{295}{x^{3/2}}$$

$$y(37)=y(36)+y'(36)\Delta x\implies y(37)-y(36)=y'(36)\Delta x$$ $$y(65)=y(64)+y'(64)\Delta x\implies y(65)-y(64)=y'(64)\Delta x$$