# What is the approximate value of a local maximum for the polynomial?

We need to calculate at least the second derivative of a polynomial, to know about the maxima or minima of the function.

## Answer: f ''(x_{0}) < 0 is the condition for all values of x = x_{0}, where the polynomial will have a local maximum.

If the second derivative of the function is zero, then there is no maxima or minima at that point in the curve.

**Explanation: **

To find the local maximum of a polynomial, we need to find the slope of the points where its value is zero.

f '(x) = 0

Let this value correspond to the point x = x_{0} on the polynomial curve.

Now we need to check for the local maximum, by applying the following condition on the second derivative of the function.

f ''(x) at ( x = x_{0} ) should be less than zero so to form a local maxima at x = x_{0}

( Representation of Global maxima in a graph)

### Thus, f ''(x_{0}) < 0 is the condition for all values of x = x_{0}, where the polynomial will have a local maximum.

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