Thread: 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.

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.

is a tangent line approximation of

is concave up ... a tangent line approximation of would be less than the actual value of because the tangent line lies beneath the curve.