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Suppose 12 is a differentiable increasing function for all x. Which number is the larger and why? 12 or 12313?

I believe f(x) must be concave up everywhere since the derivative is increasing, but I am not sure how to figure out which of those is larger based on that. Would the tangent like approximation be 12 or 12313?

Thank you!

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1 Answer 1

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The tangent line approximation at $x=4$ is $f(4)+f'(4)(x-4)$. You probably mean $x-4$ by $\Delta x$. It cannot be $f(4+\Delta x)$ as this can not be linear-a straight line does not have increasing derivative.

You are right that $f(x)$ is concave up everywhere. Does that mean it is above or below the tangent line?

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if its concave up then this would mean that f(x) is above the tangent line, so would this would make the tangent line approximation less I do believe? –  user59714 Feb 13 '13 at 23:47
    
@user59714: that is correct. –  Ross Millikan Feb 14 '13 at 0:03
    
thanks a bunch! :) –  user59714 Feb 14 '13 at 0:04

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