Welcome to Live Chat
Welcome to LiveWebTutors Services, World's leading Academic solutions provider with Millions of Happy Students.
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.
My research paper has been done from Livewebtutors. Great work, will recommend it for all.
26 Feb 2021
Ana
Thanks to the writer to handle my literature work. Super quick and smooth service.
26 Feb 2021
Harley
I was not so confident about the work done by this portal. But after the grades, I stand corrected.
26 Feb 2021
Juliet
Best paraphrasing service available at Livewebtutors. Removed my plagiarized work within half a day.
26 Feb 2021
Tessa
Accounts homework was well taken care of. Thanks to the expert who did it, youâ€™re good.
26 Feb 2021
Leila