Get the Accurate Solutions for 12th Business Maths Exercise 8.1

Get the Accurate Solutions for 12th Business Maths Exercise 8.1

If you’re a 12th-grade business maths student, you know how challenging it is to solve mathematical problems. However, with the right guidance and tools, you can master the subject and ace your exams.

In this article, we will discuss Exercise 8.1 of 12th-grade business maths, which deals with ‘Application of Derivatives.’ We will provide you with accurate solutions to the exercise, along with helpful insights to make the problem-solving process less daunting.

Introduction

Exercise 8.1 is an essential component of your 12th-grade business maths syllabus. It involves using the basic concepts of derivative to solve practical problems. The exercise covers various topics, including tangents and normals to curves, increasing and decreasing functions, and maxima and minima of functions.

We understand that as a student, you may encounter several difficulties while solving Exercise 8.1. The primary challenges include the complexity of the problems, the need for accurate calculations, and the lack of proper guidance. However, with the right approach, you can master these problems and score well in your exams.

Body

Here are the solutions to Exercise 8.1 of 12th-grade business maths:

Question 1: Find the equation of the tangent and normal to the curve y = x^3 – 3x + 1 at x=1.

Solution: We know that the slope of the tangent and normal to the curve at a given point is the derivative of the curve at that point.
Thus,

The derivative of y = x^3 – 3x + 1 is d/dx(y) = 3x^2 – 3
At x = 1, d/dx(y) = 0
Therefore, the equation of the tangent is y = mx + c, where m = d/dx(y) at x=1, and c = y – mx (substitute x and y values at x =1)

m = 3(1)^2 – 3 = 0
y = (0)(x) + c, At x=1, y = (1) – 3 +1 = -1
Hence the equation of the tangent is y=-1.

The slope of the normal at x=1 is (-1/0)= infinity. Therefore, the equation of the normal is x=1.

Question 2: Prove that the function f(x) = x^3 + 7x – 6 is increasing on R.

Solution: We need to show that for all x1 and x2, if x1Conclusion

In conclusion, Exercise 8.1 of 12th-grade business maths may seem challenging at first, but with the right tools and guidance, you can solve the problems easily. In this article, we provided you with accurate solutions to Exercise 8.1, along with an insight that can be helpful to you in your exams. We hope that our article has shed some light on the complexity of Exercise 8.1 and made it easier for you to master this topic.