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October 25th, 2014, 02:12 PM   #1
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Concavity examples?

What does a graph that has an inflection point and is rising everywhere look like? a stretched out S?

What does a concave down graph with NO highest point look like?

Also, I need to sketch a graph with two inflection points and EXACTLY one place where the tangent line has slope 0.

Thank you for your time.

Last edited by Omnipotent; October 25th, 2014 at 02:26 PM.
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October 25th, 2014, 02:27 PM   #2
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Quote:
Originally Posted by Omnipotent View Post
What does a graph that has an inflection point and is rising everywhere look like? a stretched out S?
look at the graph of $\displaystyle y = x^3$

Quote:
What does a concave down graph with NO highest point look like?
look at the graph of $\displaystyle y = -e^x$
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October 25th, 2014, 02:43 PM   #3
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[QUOTE=skeeter;210468]look at the graph of $\displaystyle y = x^3$


but its not rising at x=0 no?
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October 25th, 2014, 02:54 PM   #4
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[QUOTE=Omnipotent;210472]
Quote:
Originally Posted by skeeter View Post
look at the graph of $\displaystyle y = x^3$


but its not rising at x=0 no?
$\displaystyle y = x^3$ is increasing for all x because for $\displaystyle x_1 > x_2 \, , \, x_1^3 > x_2^3$ ... see the definition of IncreasingFunction

If you're looking for a function with an inflection point where $\displaystyle f'(x) > 0$ for all x, then look at $\displaystyle y = \arctan{x}$
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