Q. 78 - Calculus

Question

Lars was $20$ inches tall when he was born, and six foot one when he died at age $83$. Use the Intermediate Value Theorem to show that there must have been some point in Lars’s life at which his height in inches was equal to his age in years. (Hint: Think about when the difference between his height and age is zero.) 

Step-by-Step Solution

Answer

Therefore, using the Intermediate Value Theorem we showed that there must have been some point in Lars’s life at which his height in inches was equal to his age in years. 

Step 1. Given Information

Height of Lars when he was born $=20$ inches

Height of Lars when he died at $83=6$ feet

We need to use the Intermediate Value Theorem to show that there must have been some point in Lars’s life at which his height in inches was equal to his age in years. 

Step 2. Using Intermediate Value Theorem

Let the height of Lars be $70$ inches when he is $70$.

Therefore, by the Intermediate Value Theorem there is some point in Lars's life at which his height in inches was equal to his age in years.