Question

A bicyclist is riding on a path modeled by the function f(x) = 0.03(10x − x2), where x and f(x) are measured in miles. Find the rate of change of elevation at x = 1.

Answer 1

Answer: $0.024\ \text{miles per sec}$

Step-by-step explanation:

Given

Path is changing according to the function $f(x)=0.03(10x-x^2)$

Rate of change of the elevation is given by the derivative of the function

$\Rightarrow f'(x)=0.03(10-2x)$

At $x=1\ f'(x) \ \text{is}$

$\Rightarrow f'(x=1)=0.03(10-2\times 1)\\\Rightarrow f'(x=1)=0.03(8)\\\Rightarrow f'(x=1)=0.24\ \text{miles per sec}$