If f(x) attains a local minimum at x=c,

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
">f '(c) = 0

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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