JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(M\) and \(m\) be respectively the local maximum and the local minimum values of the function, \(f(x) = \,2{x^3} - 9{x^2} + 12x + 5\) in the interval \([0, 3].\) Then \(M-m\) is equal to
- A \(1\)
- B \(5\)
- C \(4\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
Here, \(f(x)=2 x^{3}-9 x^{2}+12 x+5\) \(\Rightarrow f^{\prime}(x)=6 x^{2}-18 x+12=0\) For maxima or minima put \(f^{\prime}(x)=0\) \(\Rightarrow x^{2}-3 x+2=0\) \(\Rightarrow x=1\) or \(x=2\) Now, \(f^{\prime \prime}(x)=12 x-18\)…
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 Maths
- Consider :\(f\left( x \right) = {\tan ^{ - 1}}\left( {\sqrt {\frac{{1 + \sin x}}{{1 - \sin x}}} } \right),x \in \left( {0,\frac{\pi }{2}} \right)\) A normal to \(y = f\left( x \right)\) at \(x = \frac{\pi }{6}\) also passes through the point :JEE Mains 2016 Hard
- Let the area of the region enclosed by the curve \(\mathrm{y}=\min \{\sin \mathrm{x}, \cos \mathrm{x}\}\) and the \(\mathrm{x}\)-axis between \(\mathrm{x}=-\pi\) to \(\mathrm{x}=\pi\) be \(\mathrm{A}\). Then \(\mathrm{A}^2\) is equal to ...........JEE Mains 2024 Hard
- The sum of the squares of the lengths of the chords intercepted on the circle, \(x^2 + y^2 = 16\), by the lines, \(x + y = n\), \(n \in N\), where \(N\) is the set of all natural numbers isJEE Mains 2019 Hard
- For which of the following ordered pairs \((\mu, \delta)\) the system of linear equations \(x+2 y+3 z=1\) ; \(3 x+4 y+5 z=\mu\) ; \(4 x+4 y+4 z=\delta\) is inconsistent?JEE Mains 2020 Hard
- If the greatest value of the term independent of \(^{\prime}x^{\prime}\) in the expansion of \(\left(x \sin \alpha+a \frac{\cos \alpha}{x}\right)^{10}\) is \(\frac{10 !}{(5 !)^{2}}\), then the value of \(' a^{\prime}\) is equal to:JEE Mains 2021 Hard
- Let \(A=I_2-2 \mathrm{MM}^{\mathrm{T}}\), where \(\mathrm{M}\) is real matrix of order \(2 \times 1\) such that the relation \(M^T M=I_1\) holds. If \(\lambda\) is a real number such that the relation \(\mathrm{AX}=\lambda \mathrm{X}\) holds for some non-zero real matrix \(X\) of order \(2 \times 1\), then the sum of squares of all possible values of \(\lambda\) is equal to :JEE Mains 2024 Hard
More PYQs from JEE Mains
- Let \(\vec a\, = \,\hat i\, + \,\hat j\, + \,\sqrt 2 \hat k,\,\,\vec b\, = \,{b_1}\hat i\, + \,{b_2}\hat j\, + \sqrt 2 \hat k\) and \(\vec c\, = \,5\hat i\, + \,\hat j + \sqrt 2 \hat k\) be three vectors such that the projection vector of \(\vec b\) on \(\vec a\) is \(\vec a\). If \(\vec a\, + \vec b\) is perpendicular to \(\vec c\) , then \(\left| {\vec b} \right|\) is equal toJEE Mains 2019 Hard
- For \(n \in N\), let \(S _{ n }=\left\{ z \in C :| z -3+2 i |=\frac{ n }{4}\right\}\) and \(T _{ n }=\left\{ z \in C :| z -2+3 i |=\frac{1}{ n }\right\}\) Then the number of elements in the set \(\left\{ n \in N : S _{ a } \cap T _{ n }=\phi\right\}\) is.JEE Mains 2022 Hard
- Let \(a,b \in R,\left( {a \ne 0} \right)\). if the function \(f\) defined as \(f\left( x \right)\left\{ \begin{array}{l}
\frac{{2{x^2}}}{a}\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,\,0 \le x < 1\,\,\,\\
a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,\,1 \le x < \sqrt 2 \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\
\frac{{2{b^2} - 4b}}{{{x^3}}}\,\,\,,\,\,\,\,\,\sqrt 2 \le x < \infty
\end{array} \right.\,\,\,\,\) is continuous in the interval \(\left[ {0,\infty } \right)\) , then an ordered pair \((a, b)\) isJEE Mains 2016 Hard - Let a function \(f:\left( {0,\infty } \right) \to \left( {0,\infty } \right)\) be defined by \(f\left( x \right) = \left| {1 - \frac{1}{x}} \right|\). Then \(f\) isJEE Mains 2019 Hard
- The number of four letter words that can be formed using the letters of the word \(BARRACK\) isJEE Mains 2018 Hard
- The variance of first \(50\) even natural numbers isJEE Mains 2014 Medium