#### Question

Write sufficient conditions for a point x = c to be a point of local maximum.

#### Solution

We know that at the extreme points of a function f(x), the first order derivative of the function is equal to zero, i.e.

`f '(x) = 0 " at "x = c`

`⇒ f '(c) = 0`

Also, at the point of local maximum, the second order derivative of the function at the given point must be less than zero, i.e.

`f''(c) < 0`

`f''(c) < 0`

Is there an error in this question or solution?

Solution Write Sufficient Conditions for a Point X=C to Be a Point of Local Maximum. Concept: Graph of Maxima and Minima.