Question

How do you find the local extrema of a function?

Answer 1

Hint:The values of the independent variable are plotted on the x-axis of the graph and the values of the dependent variable are plotted on the y-axis. When we observe the curve obtained on plotting the given function on the graph, the values of the independent variable at which the function reaches a peak are called the local maxima or local minima of the function.

Complete answer:
For finding the local maxima of a function, we have to first find the derivative of the given function and then put it equal to zero. On solving the obtained equation, we will get the critical points. Then we will find the second derivative of the given function and then plug in the critical values.

The values at which the second derivative comes out to be smaller than zero are called the points of local maxima and the values at which the second derivative comes out to be greater than zero are called the points of local minimum.

Note:A function is defined as an algebraic expression in which one variable is expressed in terms of the other variable, such that the value of one variable changes as the value of the other value changes. The variable quantity whose value changes with the other is known as the dependent variable and the other variable is known as an independent variable.

The value of the independent variable at which the value of the dependent variable comes out to be maximum is known as the maxima of the function, and the value of the independent variable at which the value of the dependent variable comes out to be minimum is known as the minima of the function.