MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
A smooth function g is graphed near x=2. A student considers the slope of the secant line through the points (2,g(2)) and (2+h,g(2+h)). Which of the following best describes what happens to that slope as h approaches 0?
(a) It approaches 0 because the horizontal change h becomes negligible.
(b) It has no single limit, since the quotient oscillates between positive and negative values.
(c) It becomes the exact slope of the tangent line at x=2 as the two points merge.
(d) It grows without bound; the secant line becomes vertical as h approaches 0.