How to determine whether a function has a minimum or maximum value?
Maxima and minima are very important and interesting concepts in the field of mathematics. Finding the maximum or minimum value of a function can be done in various ways like using graphical techniques, using calculus etc. We will have a look at an example in which we have to determine whether a function has a maximum or a minima value.
Answer: To determine whether a function has a minimum or maximum value, we have to double differentiate the function and check whether it has a negative or a positive value in the given domain.
Let us understand how we arrived at the answer.
Let us understand this with the help of an example.
Let us assume a function f(x) = -3x2 + 4x + 7
For that, firstly, we have to differentiate the function two times.
⇒f'(x) = -6x + 4
⇒f''(x) = -6
Here, we find that the double derivative of the function is a constant -6. Hence, it is negative.
Hence, this function has a maximum.
Alternately, if the double derivative comes out to be positive for any function, then it has a minimum.