-Given the following graph of h(x), identify:
Link: http://i55.tinypic.com/bg8nf7.jpg
a.) The intervals where h(x) is increasing and decreasing
b.) The local maximum and minimum points of h(x)
c.) The intervals where h(x) is concave up and concave down
d.) The inflection points of h(x)
e.) Sketch the graphs of h^' (x) and h"(x).
Start by thinking about (or reviewing) the definitions of the things you have been asked to find. Then show what you have tried and say where you are stuck.Originally Posted by razr
Given the following graph of h(x), identify:
Link: http://i55.tinypic.com/bg8nf7.jpg
a.) The intervals where h(x) is increasing and decreasing
b.) The local maximum and minimum points of h(x)
c.) The intervals where h(x) is concave up and concave down
d.) The inflection points of h(x)
e.) Sketch the graphs of h^' (x) and h"(x).
This is really just a matter of definitions- no calculation required. Do you understand what "increasing" and "decreasing" mean? Do you understand what "maximum", "minimum", "concave up", "concave down", and "inflection point" mean? If you know what those mean, it is just a matter of looking at the graph and seeing where they occur. As for graphing the first and second derivative, it is, again, just a matter of knowing how the derivative is related to the tangent lines of the graph. Where is the graph steepest? What does that mean for the derivative? Where does the graph level off? What does that mean for the derivative?
Let me try to help you interpret a few of the definitions that you have in terms of the graph of a function.
If a function is increasing on an interval I, then the graph goes up as you move from left to right on I.
If a function is decreasing on an interval I, then the graph goes down as you move from left to right on I.
If a function is constant on an interval I, then the graph is a horizontal line on I.
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