Question:
If $f(x)$ attains a local minimum at $x=c$, then write the values of $f^{\prime}(c)$ and $f^{\prime \prime}(c)$.
Solution:
If f(x) attains a local minimum at x = c, then the first order derivative of the function at the given point must be equal to zero, i.e.
f '(x) = 0 at x = c
The second order derivative of the function at the given point must be greater than zero, i.e.
$f^{\prime \prime}(C)>0$
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