Respuesta :
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) = [tex]\lim_{x \to 0} \frac{f(x+h)-f(x)}{h}[/tex] 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.
The relationship between the slope and the derivative of f(x) at x = a is given by;
Option B: The derivative of f(x) at x equals a equals the slope of the function at x equals a.
In mathematics and calculus to be precise, we know that the derivative of a function is defined as the rate of change of a function with respect to a variable.
For example, we want to find the derivative of the function; y = 3x² + 2x + 5
The derivative will be;
dy/dx = 6x + 2
So we see that it is the rate of change of the function which is dy with respect to the variable x.
Now, applying it to our question, the derivative of f(x) at x = a means we are putting a for the variable x after finding the derivative.
This means if we are talking about the slope, it means the slope is the value of dy/dx when x = a.
The only option that corresponds with our answer is Option B.
Read more at; https://brainly.com/question/14295614
