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 ''(x0) < 0 is the condition for all values of x = x0, 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.
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 = x0 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 = x0 ) should be less than zero so to form a local maxima at x = x0
( Representation of Global maxima in a graph)
Thus, f ''(x0) < 0 is the condition for all values of x = x0, where the polynomial will have a local maximum.