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# If F(X) Attains a Local Minimum at X=C, Then Write the Values of F' (C) and F'' (C). - Mathematics

#### Question

If f(x) attains a local minimum at x = c, then write the values of f' (c) and f'' (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''(c) > 0
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