1. The slope of the tangent line to a function at a point is equivalent to __.

Question

a. the slope of the secant at that point
b. the slope of the cosecant at that point
c. the rate of change of the function at that point
d. the slope of the secant near that point

I'm having a hard time understanding this and can't decide between a. and c. Which one is it and why?

Answer 1

The answer is c.

A secant line is a line passing through 2 points of a function; since the tangent line only goes through one point, the slope of the tangent line to a function can't properly be defined as the slope of the secant at that point, because you haven't specified the other point on the graph