The graph of a differentiable function has the following property at : the slope of…
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The graph of a differentiable function f has the following property at x=3: the slope of f is negative for x<3, zero at x=3, and positive for x>3. Which conclusion about the accumulation function g(x)=∫0xf(t)dt is most strongly supported by this information?
(a) g has a local minimum at x=3 because f attains a local minimum there.
(b) g is decreasing for x<3 and increasing for x>3 because f′(x) changes from negative to positive at x=3.
(c) g has a point of inflection at x=3 because its concavity changes sign there.
(d) g has a local maximum at x=3 because its derivative changes from decreasing to increasing.