Explain the relationship between the slope and the derivative of f(x) at xequalsa. Choose the correct answer below. A. The slope of the function at xequalsa describes the rate of change for the derivative of f(x) at xequalsa. B. The derivative of f(x) at xequalsa equals the slope of the function at xequalsa. C. The derivative of f(x) at xequalsa describes the rate of change for the slope of the function at xequalsa. D. The derivative of f(x) at xequalsa is unrelated to the slope of the function at xequalsa.

Step-by-step explanation:

We are to explain the relationship between the slope and the derivative of f(x) at x =a

B. The derivative of f(x) at xequalsa equals the slope of the function at xequalsa.

is the right answer.

The derivative of a function represents the rate of change of f(x) with respect to x

and denoted by f'(x)

f'(x) = for h>0 and very small

If we visualize a graph this value makes the function with very near points and when h tends to 0, the difference in funciton values become the slope of the tangent.

So option B is right.

Ok.

Step-by-step explanation: