Welcome to Live Chat
Welcome to LiveWebTutors Services, World's leading Academic solutions provider with Millions of Happy Students.
24x7 Support Available
To Get the Best Price Chat With Our Experts
In A Hurry? Get A Callback
We can use differentiation to find out the maxima and minimum values of the given function. Maxima and minimum values are also known as the critical values of the given function.When the first order derivative of the function that is dy / dx = 0 and the second order derivative of the function that is d^2y / dx^2 is greater than zero then the function is said to have a minimum value.
If the first order derivative of the function that is dy / dx = 0 and second order derivative of the function that is d^2y / dx^2 is less than zero then the function is said to have a maximum value. If the second order derivative of the function that is d^2 y / dx^2 is exactly equal to zero then the function is said to have both minimum or maximum values at one point.
Let us discuss maxima and minima with some of the examples.
Consider the first example be: find out the maxima and minimum values of the given function y = x^3 – 3x + 2.
The given mathematicsfunction is y = x^3 – 3x + 2. Now first let us differentiate the given function then we will get it as dy / dx = dy / dx (x^3 – 3x + 2) which is equal to dy / dx = 3x^2 – 3. Now let us equate the first differentiation to 0 then we will get it as 3x^2 – 3 = 0 in this take 3 as common then we will get it as 3(x^2 – 1) = 0 now take 3 to the left hand side then we will get it as x^2 – 1 = 0 this is in the form of (a)^2 – (b)^2 which is equals to (a + b)(a – b), so now we will get it as (x + 1)(x – 1). Now we will get the x values as 1 and -1. Now let us substitute the given x values in the given function then we will get it as if x = 1 then y = (1)^3 – 3(1) + 2 which is equals to 1 - + 2 = 0. If x = -1 then we will get it as y = (-1)^3 – 3(-1) + 2 which is equals to -1 + 3 + 2 = 4. These are known as stationary points. Now let us find out second order derivative then we will get it as d^2y / dx^2 = 6x. in this if we substitue x = -1 then we will get it as 6(-1) = -6 which is less than 0 so at this point the function has maximum value. If we substitute x = 1 we will get it as 6(1) = 6 which is greater than 0 so at this point the function has minimum value.
There is no deadline that can stop our writers from delivering quality assignments to the students.
Get authentic and unique assignments by using our 100% plagiarism-free services.
The experienced team of Live web tutors has got your back at all times of the day. Get connected with our customer support executives to receive instant and live solutions for your assignment problems.
We can build quality assignments in the subjects you're passionate about. Be it Engineering and Literature or Law and Marketing we have an expert writer for all.
Get premium service at a pocket-friendly rate. At live web tutors, we understand the tight budget of students and thus offer our services at highly affordable prices.
I recently got a presentation made by the experts of this platform. They provided an excellent service to me. The academic tone was maintained throughout the document comprehensively. The expert had a good control over the details of the presentation. Thank you for your incredible assistance.
23 Nov 2020
It is great to know that now I can rely on someone for my complicated academic assignments. I got my networking assignment composed by them and the author did a wonderful job. All the experts are very knowledgeable and helpful. Thank you for this exceptional experience.
23 Nov 2020
All my expectations with my Economics assignment were met perfectly. From my experience, this is a secure and efficient platform. Definitely try ordering your assignment from them it will be worth the value of your money.
23 Nov 2020
To date, I have ordered multiple assignments from this platform. They have saved my grades many times. Recently I ordered a management assignment from them. Their service is wonderful and the experts are extremely helpful. Thank you for making my academic journey peaceful.
23 Nov 2020
Thank you so much for the brilliantly done programming assignment solution. I was often stressed with the short deadlines; however, I won’t be anymore. All thanks to the experts of this platform I am extremely satisfied with the quality delivered to me and I even scored a good grade for it.
23 Nov 2020