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Hi I have a quick question I'm hoping someone could help me iron out. Below is a homework question I'm working on, and I need help with part (b). The answer it seems to me is "less than", and not "greater than". The reason I say this is because the tangent lines between A to B look steeper than the tangent line at B. However, I'm being told it's grater than. Could someone point out my flaw in thinking, please?

Post-edit: I am rocking like 4 hours of sleep and I'm a little dizzy. I just realized I misread the question. Sorry about taking up space. However, I won't delete it in the event this could help someone.

Post-correction: since the secant line between A and B is steeper than the tangent line at B, the rate of change between A and B is greater than instantaneous rate of change at B.

Special shout out to cnick. Thank you

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The average rate of change between A and B is the slope of the line that connects A and B. The rate of change at B is the slope of the tangent line. Since the function is concave down at the point B, we know that the slope of the tangent line is decreasing. So the average rate of change between A and B is greater than the instantaneous rate of change at B.

To address your confusion, steeper slope means greater rate of change

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  • $\begingroup$ Thank you! I just realized I misread the problem :( $\endgroup$ – Astro Jun 12 '14 at 1:44

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