Which statement correctly relates the slope of the graph of the first derivative to…
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Which statement correctly relates the slope of the graph of the first derivative f′ to the value of the second derivative f′′ at a point where both derivatives exist?
(a) If the slope of f′ is positive at the point, then f′′(x)<0.
(b) If the slope of f′ is zero at the point, then f′′(x) must be negative.
(c) If the slope of f′ is positive at the point, then f′′(x)>0.
(d) If the slope of f′ is negative at the point, then f′′(x)>0.