help@askiitians.com

1800-150-456-789

Differential Calculus> Image attached Show by LMVT and taking f(...

question mark

Image attached
Show by LMVT and taking f(x) = log x that ( question attached in image)

Drake , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:

$f(x) = log(x)$

Interval = [a, b]

Let ‘c’ be the point in the interval.

Then, by LMVT

$f'(c) = \frac{f(b)-f(a)}{b-a}$

$f'(c) = \frac{log(b)-log(a)}{b-a}$

$f'(x) = \frac{1}{x}$

$f''(x) = \frac{-1}{x^{2}}<0$

-> f’(x) is always decreasing. So, we have

$f'(b) < f'(c) < f'(a)$

$\frac{1}{b} < \frac{log(\frac{b}{a})}{b-a} < \frac{1}{a}$

$\frac{b-a}{b} < log(\frac{b}{a}) < \frac{b-a}{a}$

$1-\frac{a}{b} < log(\frac{b}{a}) < \frac{b}{a}-1$

Thanks & Regards

Jitender Singh

IIT Delhi

askIITians Faculty

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?

differential calculus

1 Answer Available

Last Activity: 2 Years ago

Find dy/DX when y=x^sinx+sin-1√x.

Please give me the solution of this problem.

differential calculus

0 Answer Available

Last Activity: 2 Years ago

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

differential calculus

0 Answer Available

Last Activity: 2 Years ago

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

differential calculus

0 Answer Available

Last Activity: 3 Years ago

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

differential calculus

0 Answer Available

Last Activity: 3 Years ago

View all Questions