Let be a differentiable function such that for all in the interval
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f be a differentiable function such that f′′(x)<0 for all x in the interval (1,5). Which statement about the graph of f on (1,5) is most accurate?
(a) It has horizontal tangent lines on (1,5) because f′′(x)<0 implies f′(x)=0 there.
(b) It is concave up on (1,5) because the slopes of the tangent lines are decreasing.
(c) It is concave down on (1,5) because the slopes of the tangent lines are decreasing.
(d) It is linear on (1,5) because the second derivative is constant on that interval.