Practise Problems on Maxima and Minima
Problem 1: Find the maximum and minimum values of the function f(x) = 2x3 – 3x2 – 12x + 1 on the interval [-2, 3].
Problem 2: Determine the critical points of the function g(x) = x4 – 4x3 + 6x2 and classify them as local maxima, local minima, or saddle points.
Problem 3: Consider the function h(x) = ex – 4x2. Find all the critical points and determine whether they correspond to local maxima, local minima, or neither.
Problem 4: A rectangular piece of cardboard measuring 8 inches by 12 inches has squares cut out of its corners, and the sides are folded up to form an open box. Find the dimensions of the squares that should be cut out to maximize the volume of the box.
Problem 5: Given the function j(x) = x3 – 12x2 + 36x + 1, find the intervals where the function is increasing and decreasing.
Maxima and Minima in Calculus
Maxima and Minima in Calculus is an important application of derivatives. The Maxima and Minima of a function are the points that give the maximum and minimum values of the function within the given range. Maxima and minima are called the extremum points of a function.
This article explores the concept of maxima and minima. In addition to details about maxima and minima, we will also cover the types of maxima and minima, properties of Maxima and Minima, provide examples of maxima and minima, and discuss applications of Maxima and Minima.
Table of Content
- Maxima and Minima of a Function
- Types of Maxima and Minima
- Relative Maxima and Minima
- Absolute Maxima and Minima
- How to Find Maxima and Minima?
- Applications of Maxima and Minima
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