A solution curve to a certain differential equation is concave down for every (that is, )
MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A solution curve to a certain differential equation is concave down for every x>0 (that is, y′′(x)<0 for all x>0). Starting at the point (0,1), successive tangent-line steps of equal positive length are taken to approximate the solution values. For x>0, will each tangent-line estimate be an overestimate or an underestimate of the true solution values? Briefly state your conclusion.