Question

Suppose f has a continuous positive second derivative for all x. Which of the following is smaller?

a.) f(1 + Δx)
b.) f(1) + f '(1) Δx

Answer 1

Hint: since \(f\) has a positive second derivative, it is concave up. (a) is the actual value of \(f\) at \(1 + \Delta x\) and (b) is the tangent-line approximation about \(1\).

Answer 2

Thanks for the hint.

Answer 3

This is of course assuming that \(\Delta x \approx 0\).

Answer 4

I'm sure it is.