Let \( f(x) \) be positive, continuous, and differentiable on the interval \( (a, b) \) and \( \...

Channel:
PW Solutions
Subscribers:
445,000
Published on ● Video Link: https://www.youtube.com/watch?v=tb3bF_hVzmA


Duration: 7:01
31 views
0

Let \( f(x) \) be positive, continuous, and differentiable on the interval \( (a, b) \) and \( \lim _{x \rightarrow a} f(x)=1, \lim _{x \rightarrow b} f(x)=3^{1 / 4} \). If \( f^{\prime}(x) \) \( \geq f^{3}(x)+\frac{1}{f(x)} \) then the greatest value of \( b-a \) is
(a) \( \frac{\pi}{48} \)
(b) \( \frac{\pi}{36} \)
(c) \( \frac{\pi}{24} \)
(d) \( \frac{\pi}{12} \)
πŸ“²PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-06-09If \( f(x)=x^{5}+5 x-1 \) then \( \int_{5}^{41} \frac{d x}{\left(f^{-1}(x)\right)^{5}+5 f^{-1}(x...
2023-06-09If \( \int_{-20}^{-10}\left(\frac{x^{2}-x}{x^{3}-3 x+1}\right)^{2} d x+\int_{\frac{1}{21}}^{\fra...
2023-06-09\( S_{1}: \) If \( n \) is a positive integer then \[ \begin{array}{l} \int_{0}^{n \pi}\left|\fr...
2023-06-09The value of \( \int_{0}^{I}\left(\prod_{r=1}^{n}(x+r)\right)\left(\sum_{k=1}^{n} \frac{1}{x+k}\...
2023-06-09Evaluate: \( I=\int_{0}^{1} \frac{\tan ^{-1} a x}{x \sqrt{1-x^{2}}} d x \)
2023-06-09\[ \text { If } \begin{array}{l} \int_{0}^{1}\left(\sum_{r=1}^{2013} \frac{x}{x^{2}+r^{2}}\righ...
2023-06-09If \( f(x)=\int_{0}^{1} e^{|t-x|} d t \) where \( (0 \leq x \leq 1) \), then maximum value of \(...
2023-06-09Match the following Column-I with Column-II \begin{tabular}{|l|l|l|l|} \hline \multicolumn{2}{|c...
2023-06-09\( \lim _{x \rightarrow 0} \frac{\int_{0}^{x^{2}}\left(\tan ^{-1} t\right)^{2} d t}{\int_{0}^{x^...
2023-06-09\[ \int_{a}^{b} x^{n-1} \frac{\left((n-2) x^{2}+(n-1)(a+b) x+n a b\right)}{(x+a)^{2}(x+b)^{2}} d...
2023-06-09Let \( f(x) \) be positive, continuous, and differentiable on the interval \( (a, b) \) and \( \...
2023-06-09Evaluate: \( \int_{0}^{1} \frac{d x}{\left(5+2 x-2 x^{2}\right)\left(1+c^{2-4 x}\right)} \)
2023-06-09Evaluate: \( \int_{0}^{\infty} \frac{\ln x d x}{x^{2}+2 x+4} \)
2023-06-09Evaluate: \( \int_{\pi / 6}^{\pi / 4}\left[\frac{\sec x+\operatorname{cosec} x-\sec x \operatorn...
2023-06-09Evaluate \( \int_{0}^{1} \frac{d x}{x^{2}+2 x \cos \alpha+1} \) where \( -\pi\alpha\pi \)
2023-06-09Evaluate \( \int_{1 / 3}^{3} \frac{\sin ^{1} \frac{x}{\sqrt{1+x^{2}}}}{x} d x \)
2023-06-09Suppose that \( f, f^{\prime} \) and \( f^{\prime \prime} \) are continuous on \( [0, \ln 2] \) ...
2023-06-09Evaluate: \( \lim _{n \rightarrow \infty}\left({ }^{2 n} C_{n}\right)^{1 / n} \)
2023-06-09\( \int_{0}^{2 n \pi}\left(|\sin x|-\left[\left|\frac{\sin x}{2}\right|\right]\right) d x \quad[...
2023-06-09Find the value of definite integral \[ \frac{\int_{0}^{\pi}(\sqrt[2013]{\cos x}+\sqrt[2013]{\sin...
2023-06-09\( \int_{0}^{\pi / 2} \frac{\cos x-\sin x}{1+\sin x \cos x} d x= \)