Question

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

Answer 1

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`