JEE Advanced · Mathematics · 25. AOD
The maximum value of the function \(f(x)=2 x^3-15 x^2+36 x-48\) on the set \(A=\left\{x \mid x^2+20 \leq 9 x\right\}\) is
- A 5
- B 10
- C 9
- D 11
Answer & Solution
Correct Answer
(A) 5
Step-by-step Solution
Detailed explanation
Given, \(\quad A=\left\{x \mid x^2+20 \leq 9 x\right\}\) \(=\{x \mid x \in[4,5]\}\)
Now, \(f^{\prime}(x)=6\left(x^2-5 x+6\right)\)
Put \(\quad f^{\prime}(x)=0 \Rightarrow x=2,3\)
\(f(2)=-20, f(3)=-21\),
\(f(4)=-16, f(5)=7\)
From graph, maximum of \(f(x)\) on set \(A\) is \(f(5)=7\).
Now, \(f^{\prime}(x)=6\left(x^2-5 x+6\right)\)
Put \(\quad f^{\prime}(x)=0 \Rightarrow x=2,3\)
\(f(2)=-20, f(3)=-21\),
\(f(4)=-16, f(5)=7\)
From graph, maximum of \(f(x)\) on set \(A\) is \(f(5)=7\).
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Mathematics
- Let be a complex number with non-zero imaginary part. If is a real number, then the value of is ______.JEE Advanced 2022 Hard
- Let \(f\) be a non-negative function defined on the interval \([0,1]\). If \(\int_0^x \sqrt{1-\left\{f^{\prime}(t)\right\}^2} d t=\int_0^x f(t) d t, \quad 0 \leq x \leq 1\)
\[
\text { and } f(0)=0 \text {, then }
\]JEE Advanced 2009 Hard - Let \(a_{n}\) denote the number of all \(n\)-digit positive integers formed by the digits 0,1 or both such that no consecutive digits in them are 0 . Let \(b_{n}=\) the number of such \(n\)-digit integers ending with digit 1 and \(c_{n}=\) the number of such \(n\)-digit integers ending with digit 0 .
Question:
Which of the following is correct?JEE Advanced 2012 Hard - Let \(\alpha(a)\) and \(\beta(a)\) be the roots of the equation \((\sqrt[3]{1+a}-1) x^{2}+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0\) where \(a\) \(>-1\). Then \(\lim _{a \rightarrow 0^{+}} \alpha(a)\) and \(\lim _{x \rightarrow 0^{+}} \beta(a)\) areJEE Advanced 2012 Medium
- For \(0 < \theta < \frac{\pi}{2}\), the solution(s) of \(\sum_{m=1}^6 \operatorname{cosec}\left[\theta+\frac{(m-1) \pi}{4}\right]\) \(\operatorname{cosec}\left(\theta+\frac{m \pi}{4}\right)=4 \sqrt{2}\) is/areJEE Advanced 2009 Hard
- For how many values of , the circle and the coordinate axes have exactly three common points?JEE Advanced 2017 Medium
More PYQs from JEE Advanced
- A point object is placed at distance of \(20 \mathrm{~cm}\) from a thin planoconvex lens of focal length \(15 \mathrm{~cm}\). The plane surface of the lens is now silvered. The image created by the system is at
JEE Advanced 2006 Medium - The circular scale of a screw gauge has 50 divisions and pitch of \(0.5 \mathrm{~mm}\). Find the diameter of sphere. Main scale reading is 2 .
JEE Advanced 2006 Easy - Two uniform strings of mass per unit length \(\mu\) and \(4 \mu\), and length \(L\) and \(2 L\), respectively, are joined at point \(\mathrm{O}\), and tied at two fixed ends \(\mathrm{P}\) and \(\mathrm{Q}\), as shown in the figure. The strings are under a uniform tension \(T\). If we define the frequency \(v_0=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}\), which of the following statement(s) is(are) correct?
JEE Advanced 2024 Medium - Let the point be the reflection of the point with respect to the line Let and be circle of radii and with centres and respectively. Let be a common tangent to the circle and such that both the circle are on the same side of If is the point of intersection of and the line passing through and then the length of the line segment is ___________.JEE Advanced 2019 Medium
- Column I showns four systems, each of the same length \(L\), for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as \(\lambda_f\). Match each system with statements given in Column II describing the nature and wave length of the standing waves.
JEE Advanced 2011 Hard - If \(|z|=1\) and \(z \neq \pm 1\), then all the values of \(\frac{z}{1-z^2}\) lie onJEE Advanced 2007 Medium