# Math Help - Which of the following is larger?

1. ## Which of the following is larger?

Suppose f has a continuous positive second derivative for all x. Which of the following is larger?
f(1 + deltax)
f(1) + f '(1)*deltax

I need an explanation, my first instinct is to think that it is the first choice because of the positive second derivative.

2. Originally Posted by Latszer
Suppose f has a continuous positive second derivative for all x. Which of the following is larger?
f(1 + deltax)
f(1) + f '(1)*deltax

I need an explanation, my first instinct is to think that it is the first choice because of the positive second derivative.
$f(1) + f'(1)(\Delta x)$ is a tangent line approximation of $f(1 + \Delta x)$

$f(x)$ is concave up ... a tangent line approximation of $f(1 + \Delta x)$ would be less than the actual value of $f(1 + \Delta x)$ because the tangent line lies beneath the curve.