Suppose a differentiable function satisfies for every in the interval
MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Suppose a differentiable function f satisfies f′′(x)>0 for every x in the interval [a,a+h]. A single tangent-line step of length h is taken from the point (a,f(a)) to approximate f(a+h). Which statement about the resulting estimate is true?
(a) It is greater than the actual value because the graph is concave up on the interval.
(b) The estimate will be greater than the actual value when h<0 and less when h>0.},{
(c) It is less than the actual value because the graph is concave up on the interval.
(d) Insufficient information is given to determine whether the estimate is less than or greater than the actual value.