wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

How do you find Maximum In Calculus?


Open in App
Solution

We can find the maximum, minimum values of functions by two methods:

  1. By plotting the graph of the function
  2. By using derivatives of the function.

Method 1. A maximum is a high point and a minimum is a low point of the graph. In a smoothly changing function a maximum or minimum is always where the value of slope is zero (except for a saddle point) and the value of slope can be found by the derivative of the function.

Saddle point: A saddle point is a point at which the function has neither a maximum nor a minimum value.

Method 2. Take f(x) to be a function of x. Then the value of x for which the derivative of f(x) with respect to x is equal to zero corresponds to a maximum, a minimum or an inflexion point of the function f(x).

The second derivative demonstrates whether a point with zero first derivative is maximum, a minimum, or an inflexion point,

For a maximum, dydt=0and d2ydx2<0 that means the slope of the curve is at first positive, then goes through zero to become negative.

For a minimum, dydt=0and d2ydx2>0 that means the slope of the curve is at first negative, then goes through zero to become positive.

For an inflexion point, dydt=0and d2ydx2=0 It represents a point where the curvature is changing its sense.

Hence, we can find the maximum by derivative or by plotting graph of the given function.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Line and a Parabola
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon