Application Of Differentiation

Gbogbo ọrọ náà

Welcome to the course material on the Application of Differentiation in General Mathematics. This topic delves into the practical use of differentiation, a fundamental concept in calculus, to solve various problems involving rate of change, maxima and minima. Differentiation enables us to analyze how a function changes as its input changes, allowing us to determine critical points, where the function reaches its maximum or minimum values.

One of the key objectives of this topic is to equip you with the skills to solve real-world problems that involve finding rates of change. For example, in physics, differentiation is used to calculate the velocity and acceleration of an object by analyzing its position function with respect to time. By understanding the concept of rate of change, you will be able to tackle optimization problems efficiently.

Furthermore, through the study of differentiation of explicit algebraic and simple trigonometrical functions such as sine, cosine, and tangent, you will learn how to find the slopes of curves at any given point. This enables you to determine the rate at which a quantity is changing at a specific instant, a vital skill in various fields such as economics, engineering, and biology.

As we explore the topic of maxima and minima, you will discover how to identify points where a function attains its highest (maxima) and lowest (minima) values. Understanding these critical points is essential for optimizing processes and resources in practical scenarios, such as maximizing profit or minimizing costs in business applications.

Throughout this course, you will engage with problems that require the application of differentiation to analyze and solve real-world situations. By mastering the principles of rate of change, maxima, and minima, you will develop a strong foundation in calculus that can be applied across various disciplines. Get ready to embark on a journey that enhances your problem-solving skills and analytical thinking through the Application of Differentiation!

Ebumnobi

  1. Calculate the rate of change using differentiation
  2. Understand the concept of differentiation
  3. Apply differentiation to solve problems in real-life situations
  4. Determine maxima and minima of functions using differentiation

Akọmọ Ojú-ẹkọ

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Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Application Of Differentiation. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

  1. A function f(x) = 3x^2 - 6x + 2 is given. Find the rate of change of f(x) at x = 2. A. 5 B. 7 C. 9 D. 11 Answer: B. 7
  2. The function g(x) = 4x^3 - 2x^2 + 5x - 1 represents the profit made by a company at time x. Find the maximum profit. A. 10 B. 15 C. 20 D. 25 Answer: C. 20
  3. Given h(x) = 2x^4 + 6x^3 - 4x^2, find the point of inflection. A. (-1, -4) B. (0, 0) C. (1, 4) D. (2, 2) Answer: B. (0, 0)
  4. The function y(x) = 6x^2 + 4x - 3 represents the height of a ball thrown in the air. Find the maximum height the ball reaches. A. 10 B. 15 C. 20 D. 25 Answer: D. 25
  5. If f(x) = 5x^3 - 2x^2 + 3x + 2, find the local minimum of the function. A. -5 B. -2 C. 1 D. 5 Answer: A. -5

Àwọn Ìwé Tó Dáa Láti Kà

Calculus: Early Transcendentals
Calculus: Early Transcendentals
Onkọwe atẹjade: Wiley
Afọ: 2016
ISBN: 978-1133118405
Differential Equations and Their Applications
Differential Equations and Their Applications
Onkọwe atẹjade: Springer
Afọ: 2018
ISBN: 978-3030059474

Àwọn Ìbéèrè Tó Ti Kọjá

Nna, you dey wonder how past questions for this topic be? Here be some questions about Application Of Differentiation from previous years.

WAEC SSCE - General Mathematics - 2022

Ajụjụ 1 Ripọtì

Given that sin (5x-28)° = cos (3x-50)", 0°≤ x ≤ 90°, find the value of x.

Wo Idahun
JAMB UTME - Mathematics - 2023

Ajụjụ 1 Ripọtì

The area A of a circle is increasing at a constant rate of 1.5 cm2s-1. Find, to 3 significant figures, the rate at which the radius r of the circle is increasing when the area of the circle is 2 cm2.

Wo Idahun