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

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.

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?

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

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?

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.

To find the rate of change of elevation, we need to find the derivative of the function F(x) = 0.2x with respect to x.

The derivative of a function represents the rate of change of the function at a given point. In this case, it tells us how fast the elevation is changing with respect to the distance traveled by the cyclist.

To find the derivative of F(x) = 0.2x, we can use the power rule of differentiation. The power rule states that if we have a function of the form f(x) = ax^n, then its derivative is given by f'(x) = nax^(n-1).

In this case, the function is F(x) = 0.2x, where a = 0.2 and n = 1. Applying the power rule, we get:

F'(x) = 1 * 0.2x^(1-1) = 0.2

So, the rate of change of elevation is 0.2.

Now, to find the rate of change of elevation when x = 5, we substitute x = 5 into the derivative we found:

F'(5) = 0.2

Therefore, the rate of change of elevation when x = 5 is 0.2.