JEE Mains · Maths · STD 12 - 6. Application of derivatives
The sum of the absolute minimum and the absolute maximum values of the function \(f(x)=\left|3 x-x^{2}+2\right|-x\) in the interval \([-1,2]\) is
- A \(\frac{\sqrt{17}+3}{2}\)
- B \(\frac{\sqrt{17}+5}{2}\)
- C \(5\)
- D \(\frac{9-\sqrt{17}}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\sqrt{17}+3}{2}\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{ll}x^{2}-4 x-2, & \forall x \in\left(-1, \frac{3-\sqrt{17}}{2}\right) \\ -x^{2}+2 x+2, & \forall x \in\left(\frac{3-\sqrt{17}}{2}, 2\right)\end{array}\right.\) \(f^{\prime}(x)\) when \(x \in\left(-1, \frac{3-\sqrt{17}}{2}\right)\)…
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
- The sum of the \(3^{rd}\) and the \(4^{th}\) terms of a \(G.P.\) is \(60\) and the product of its first three terms is \(1000\). If the first term of this \(G.P.\) is positive, then its \(7^{th}\) term isJEE Mains 2015 Hard
- If the mean of the following probability distribution of a random variable \(X\);
is \(\frac{46}{9}\) , then the variance of the distribution is\(X\) \(0\) \(2\) \(4\) \(6\) \(8\) \(P(X)\) \(a\) \(2a\) \(a+b\) \(2b\) \(3b\) JEE Mains 2024 Hard - The complex number \(z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}\) is equal to \(.....\)JEE Mains 2023 Hard
- If \(\int_{0}^{\sqrt{3}} \frac{15 x^{3}}{\sqrt{1+x^{2}+\sqrt{\left(1+x^{2}\right)^{3}}}} d x=\alpha \sqrt{2}+\beta \sqrt{3}\), where \(\alpha, \beta\) are integers, then \(\alpha+\beta\) is equal to.JEE Mains 2022 Hard
- If \(2 \tan ^2 \theta-5 \sec \theta=1\) has exactly \(7\) solutions in the interval \(\left[0, \frac{n \pi}{2}\right]\), for the least value of \(n \in N\) then \(\sum_{\mathrm{k}=1}^{\mathrm{n}} \frac{\mathrm{k}}{2^{\mathrm{k}}}\) is equal to :JEE Mains 2024 Hard
- Let \(a, b, c, d\) be in arithmetic progression with common difference \(\lambda\). If \(\left|\begin{array}{lll} x+a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c \end{array}\right|=2\) then value of \(\lambda^{2}\) is equal to \(.....\)JEE Mains 2021 Medium
More PYQs from JEE Mains
- If a random variable x has the probability distribution
then \(P (3< x \leq 6)\) is equal tox 0 1 2 3 4 5 6 7 p(x) 0 2k k 3k \(2 k ^2\) 2k \(k ^2+ k\) \(7 k ^2\) JEE Mains 2026 Medium - Let \(y=f(x)\) represent a parabola with focus \(\left(-\frac{1}{2}, 0\right)\) and directrix \(y =-\frac{1}{2}\). Then \(S=\left\{x \in R : \tan ^{-1}\left(\sqrt{f(x)}+\sin ^{-1}(\sqrt{f(x)+1})\right)=\frac{\pi}{2}\right\}:\)JEE Mains 2023 Hard
- If \(\frac{ dy }{ dx }+2 y \tan x =\sin x , 0< x <\frac{\pi}{2}\) and \(y \left(\frac{\pi}{3}\right)=\) 0 , then the maximum value of \(y(x)\) is.JEE Mains 2022 Hard
- A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is \(\frac{1}{4}\). Three stones \(A , B\) and \(C\) are placed at the points \((1,1),(2,2)\) and \((4,4)\) respectively. Then which of these stones is \(/\) are on the path of the man ?JEE Mains 2021 Medium
- Let \(P \left( a _1, b _1\right)\) and \(Q \left( a _2, b _2\right)\) be two distinct points on a circle with center \(C (\sqrt{2}, \sqrt{3})\). Let \(O\) be the origin and \(OC\) be perpendicular to both \(CP\) and \(CQ\). If the area of the triangle \(OCP\) is \(\frac{\sqrt{35}}{2}\), then \(a _1^2+ a _2^2+ b _1^2+ b _2^2\) is equal to \(...........\).JEE Mains 2023 Hard
- \(\mathop {\lim }\limits_{y \to 0} \frac{{\sqrt {1 + \sqrt {1 + {y^4}} } - \sqrt 2 }}{{{y^4}}} = \)JEE Mains 2019 Hard