#### 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`

`f''(c) > 0`

Is there an error in this question or solution?

Solution If F(X) Attains a Local Minimum at X=C, Then Write the Values of F' (C) and F'' (C). Concept: Graph of Maxima and Minima.