Maths > Monotonicity, Maxima and Minima > 6.0 Maxima and Minima
Monotonicity, Maxima and Minima
1.0 Rolle's Theorem
2.0 Lagrange's Mean Value Theorem
3.0 Monotonicity of a function
4.0 Finding intervals of increasing and decreasing functions
5.0 Proving inequality using monotonicity
6.0 Maxima and Minima
7.0 First Derivative Test
8.0 Second Derivative Test
9.0 Absolute Maxima and Absolute Minima
10.0 Maxima and Minima of Discontinuous functions
6.1 Local Maxima and Local Minima
To find the point of local maxima or local minima, let us assume a real valued function $f(x)$ and the points $'c'$ and $'d'$ must lie inside the domain of the function.
- $f$ is having the maximum value at point $C$ in the interval $I \in (a,b)$ which is only possible when $$f(c) \geqslant f(x)$$ The point on the $X$-axis corresponding to $C$ i.e., $'c'$ is the point of maximum value of $f$ in the interval $I$ which is called as the point of local maxima or relative maxima.
- $f$ is having the minimum value at point $D$ in the interval $I \in (a,b)$ which is only possible when $$f(d) \leqslant f(x)$$ The point on the $X$-axis corresponding to $D$ i.e., $'d'$ is the point of minimum value of $f$ in the interval $I$ which is called as the point of local minima or relative minima.
