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Find the intervals of concavity and the points of inflection of the following functions: $f(x)=x^{2}-x$

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  • Test for concavity Suppose $f$ is twice differentiable on an interval I.
  • (i) If $f''(x) > 0$ for all $x \in I$, then the graph of is concerve upward (convex downward ) on I.
  • (ii) If $ f''(x) < 0$ fro all $x \in I$. then the graph of f is conceve downward ( convex upward) on I.
$f(x)=x^2-x$
$f'(x)=2x-1$
$f''(x)=2$
$f''(x) > 0 $ always => $f(x)$ is concave upward for all $ x \in R $.
There is no point of inflection.
answered Aug 5, 2013 by meena.p
 

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