Question

Which is correct? The derivative function f'(x) tells us the slope of the tangent line at each of the points (x, f(x)). The derivative function f'(x) tells us the slope of the secant line through (x, f(x)) and (x+h, f(x+h)) for h.

a) True
b) False

Answer 1

The correct option is a) True. The derivative function f'(x) tells us the slope of the tangent line at each of the points (x, f(x)). The secant line connects two points on the curve, not the tangent line.

Step-by-step explanation:

The correct option is a) True.

The derivative function f'(x) tells us the slope of the tangent line at each of the points (x, f(x)). The tangent line is a straight line that touches the curve of the function at a specific point and has the same slope as the curve at that point.

On the other hand, the secant line connects two points on the curve. In this case, the derivative function f'(x) does not tell us the slope of the secant line through (x, f(x)) and (x+h, f(x+h)) for h.