In: Math
A bicyclist is riding on a path modeled by the function
f(x) = 0.07x,
where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at
x = 5.
The rate of change of a function at any point "c" is equivalent to the slope of the line that is tangent to it. It is the derivative of the function at the point . We can make use of First Principle to find the derivative
Here
We need to evaluate the elevation at x=5 and it is given by
The rateof change of elevation at x=5 is 0.07
Now we can do this in another way
Lets start from the begining that is when x=0
Since we need to evaluate the rate of change of elevation at x=5
Hence the slope which gives the rate of change of elevation
Hence the rate of elavation at x=5 is 0.07