Question

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.

Answer 1

Answer:

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) = $\lim_{x \to 0} \frac{f(x+h)-f(x)}{h}$ 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.