Question

A cyclist is riding on a path whose elevation is modeled by the function F(X)=0.2x where x and f(x) arte measured in miles. Find the rate of change of elevation when x=5. ?

Supposed answer: ?? 1

Answer 1

since f(x) = 0.2x
df/dt = 0.2 dx/dt

That speed is independent of x, but does depend on how fast x is changing, which you have not said.

Answer 2

It is a straight line slope so i would say they depend on each other so the rate of change of elevation when x=5 would be 1?

Answer 3

You have to know dx/dt, the speed, to do this problem.

Answer 4

The derivative of 0.2x is 0.2 ! ohh so when you plug in the five is it just the same outcome 00.2? f(5)=0.2?

Answer 5

f(x) = 0.2x
f(5) = 0.2(5) = 1

if x is changing slowly, a point at (x,y) moves slowly along the line. If x is changing quickly, the point moves faster.

unless you know dx/dt, you cannot know df/dt, the rate at which f is changing. All you know is that f(x) changes 1/5 as fast as x does.