Areas and Distances James Stewart (5.1)

[gail_force_wind]

Hi,
this is more of a conceptual question regarding a question in the book I'm using. For finding the over and under estimates of a graph/function the graph/function has to be strictly increasing or decreasing (so saith my professor). But the question I'm stuck on is asking me to find the over and under estimates of a parabolic function. I checked the answer and one is there.

Can I find the OE and UE of a function/graph if it is decreasing and increasing?

If so, how?

Also, if this is possible, was my teacher wrong?

 

[tkhunny]

If it is continuous, there is always a way. Just pick the greatest or lowest value in the interval. It's not always the right or left endpoint. It may not even be an endpoint. If it is not continuous, there may still be a way,

 

[DrPhil]

Hi,
this is more of a conceptual question regarding a question in the book I'm using. For finding the over and under estimates of a graph/function the graph/function has to be strictly increasing or decreasing (so saith my professor). But the question I'm stuck on is asking me to find the over and under estimates of a parabolic function. I checked the answer and one is there.

Can I find the OE and UE of a function/graph if it is decreasing and increasing?

If so, how?

Also, if this is possible, was my teacher wrong?

If you know the vertex of the parabola, then you can treat one half of it as increasing and the other half as decreasing. Find OEs and UEs separately for the two halves. The rule for OE on one half will be the rule for UE on the other half.