If f(x) attains a local minimum at x=c, then write the values of f' (c) and f'' (c).

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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
$\Rightarrow$ f '(c) = 0

The second order derivative of the function at the given point must be greater than zero, i.e.
f ''(c) > 0

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