A differentiable function is concave up on the interval
MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A differentiable function f is concave up on the interval (1.0,1.2). An approximation to f′(1.1) is obtained from the slope of the secant line through the points (1.1−0.05,f(1.05)) and (1.1+0.05,f(1.15)). Will this approximation be an overestimate or an underestimate of f′(1.1)? Briefly explain.