Question
The body mass index is defined in Exercise 39. Draw the level curve of this function corresponding to someone who is 200 cm tall and weighs 80 kg. Find the weights and heights of two other people with that same level curve.
Step 1
In this case, we are given that the person is 200 cm tall (which is 2 m) and weighs 80 kg. So, the BMI is calculated as follows: \[BMI = \frac{m}{h^2} = \frac{80}{2^2} = 20\] Show more…
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Body mass index Draw the level curve of the body mass index function corresponding to someone who is 200 $\mathrm{cm}$ tall and weighs 80 $\mathrm{kg}$ . Find the weights and heights of two other people with that same level curve.
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The body mass index (BMI) of a person is defined by $$ B(m, h)=\frac{m}{h^{2}} $$ where $m$ is the person's mass (in kilograms) and $h$ is the height (in meters). Draw the level curves $B(m, h)=18.5$ $B(m, h)=25, B(m, h)=30,$ and $B(m, h)=40 .$ A rough guideline is that a person is underweight if the BMI is less than $18.5 ;$ optimal if the BMI lies between 18.5 and $25 ;$ overweight if the BMI lies between 25 and $30 ;$ and obese if the BMI exceeds $30 .$ Shade the region corresponding to optimal BMI. Does someone who weighs 62 kg and is 152 $\mathrm{cm}$ tall fall into this category?
Partial Derivatives
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