Question

Finding the derivative of a function at a point x gives

A.) The slope of the secant line of the function at x
B.) A line parallel to the function
C.) The slope of the tangent line of the function at x
D.)None of the above

Answer 1

C.)

Explanation:

that is exactly the definition of the derivative.

the derivative is the limit of

(f(x+h) - f(x))/((x+h) - x) = (f(x+h) - f(x))/h

with h going to 0.

this is the limit of the standard rate of change concentrated on a single point = the slope of the tangent at that point.