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## Homework Statement

x

Determine all intervals over which the function f(x)=∫√(1+t^2) dt is concave upward

1

## Homework Equations

I know concave up means the f"(x)>0, so you have to get the second derivative

## The Attempt at a Solution

f'(x)=√(1+x^) by susbituting in x

Then f"(x)=1/2*(1+x^2)^(-1/2)*2x

This is equal to:

2x/2√(1+x^2)

Then, I'm really confused on what to do next because the denominator is never zero, so would the only critical point be 0 and you check to the left and right of that?