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Q. The graph of $y=f^{\prime \prime}(x)$ for a function $f$ is shown. Number of points of inflection for $y=f(x)$ isMathematics Question Image

Application of Derivatives

Solution:

Only at $A$ and $E$
only at $D f ^{\prime \prime}( x )=0$ but does not change sign
at $x=c, f^{\prime \prime}(c)=0$ and does not change sign
$\therefore $ nothing can be said.