JEE Exam > JEE Questions > Let a, b = R be such that the function f give...
Start Learning for Free
Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at?
Most Upvoted Answer
Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 ...
Extreme Values of Function f
In this problem, we are given a function f(x) defined as t(x) = tnbx * tr^2 - ax, where a and b are real numbers. We need to determine the conditions under which the function has extreme values.
Definition of Extreme Values
An extreme value of a function occurs at a point where the derivative of the function is either zero or does not exist. These points are called critical points. To find extreme values, we need to find the critical points of the function.
Finding the Derivative of f(x)
To find the derivative of the function f(x), we can use the product rule. Let's denote t(x) as u(x) and tr^2 - ax as v(x). Applying the product rule, we have:
f'(x) = u'(x)v(x) + u(x)v'(x)
Finding the Critical Points
To find the critical points, we need to solve the equation f'(x) = 0. Let's set f'(x) = 0 and solve for x:
0 = u'(x)v(x) + u(x)v'(x)
0 = (tnbx)' * (tr^2 - ax) + tnbx * (tr^2 - ax)'
0 = (tnb)' * (tr^2 - ax) + tnb * (tr^2 - ax)'
0 = nb * (tr^2 - ax) + tnbx * (-a)
0 = nb * tr^2 - nb * ax - tnbx * a
0 = nb * tr^2 - tnbx * a - nb * ax
0 = nb * tr^2 - a * tnbx - nb * ax
0 = nb * tr^2 - ax * (tnb + nb)
ax * (tnb + nb) = nb * tr^2
ax = (nb * tr^2) / (tnb + nb)
Conditions for Extreme Values
The function f(x) has extreme values at the points where the derivative f'(x) is either zero or does not exist. From the equation we obtained for the critical points, we can see that the function will have extreme values when:
- tnb + nb ≠ 0 (to avoid division by zero)
- a ≠ 0 (to avoid a constant function)
Therefore, the conditions for extreme values of the function f(x) are:
tnb + nb ≠ 0 and a ≠ 0
These conditions ensure that the derivative f'(x) exists and is not zero, allowing us to find the critical points and determine the extreme values of the function.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at?
Question Description
Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at?.
Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at?.
Solutions for Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at? defined & explained in the simplest way possible. Besides giving the explanation of
Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at?, a detailed solution for Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at? has been provided alongside types of Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at? theory, EduRev gives you an
ample number of questions to practice Let a, b = R be such that the function f given by t(x) = tnbx )+tr^ 2 - ax, x=0 has extreme values at? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup