For a twice-differentiable function whose second derivative satisfies on an open…

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

For a twice-differentiable function whose second derivative satisfies

y''(x)>0

on an open interval containing

x=a

, does the tangent-line (linear) approximation at

x=a

give an overestimate or an underestimate of the function’s true value for

x>a

that is sufficiently close to

a