In calculus, maxima and minima are found by using the concept of derivatives. The derivatives' concept gives the information regarding the gradient, we can locate the point where the gradient is zero, and these points are considered turning points or stationary points. These points are associated with the largest or smallest values of the function. The point of minima is found whenever the double derivative is positive, whereas the point of maxima occurs whenever the double derivative is negative.
In RD Sharma Solutions for Class 12th Maths Chapter 18 maxima and minima, students first obtain knowledge on how to describe maximum and minimum values. Maximum is a point at which the value of a function is greatest, whereas minimum in maths is a point at which the value of a function is less than or equal to the value at any nearby point (local point) or an absolute minimum. Along with this, students also study about maximum and minimum values of a function in its domain.
After this, students are taught on a topic called local maxima and local minima. In case, f is a function, and D (f) is the domain of f. Let a ∈D (f). We can say that f (a) is a maximum local value on f or a local maxima if f a≥f x when x is near a. Likewise, we can say that f (a) is a local minimum value on f or a local minima if f a≤f (x) where x is near a.
Then they learn how to solve the first derivative test for local maxima and minima. Additionally, students can also learn about higher-order derivative tests. Finally, they study theorems and algorithms based on a higher derivative test.
Some more concepts covered in this chapter include point of inflection, maximum and minimum values in a closed interval, and solve applied problems on maxima and minima.