The sum of the absolute minimum and the absolute maximum values of the function ƒ(x) = |3x – x2 + 2| – x in the interval [–1, 2] is
\(\frac{\sqrt17+3}{2}\)
\(\frac{\sqrt{17}+5}{2}\)
5
\(\frac{9-\sqrt{17}}{2}\)
The Correct Option is A
Solution and Explanation
The correct answer is (A) : \(\frac{\sqrt17+3}{2}\)
ƒ(x) = |x2– 3x – 2| – x
\(∀x∈[−1,2]\)
\(f(x) = \begin{cases} x^2 - 4x - 2 & \text{if } -1 \leq x < \frac{3 - \sqrt{17}}{2} \\ -x^2 + 2x + 2 & \text{if } \frac{3 - \sqrt{17}}{2} \leq x \leq 2 \end{cases}\)
\(ƒ(x)_{max} = 3\)
\(ƒ(x)_{min}=ƒ(\frac{3−\sqrt{17}}{2})\)
\(=\frac{\sqrt{17}-3}{2}\)
Top JEE Main Mathematics Questions
- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
- If , then the general value of is:
- The general solution of
- If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____
Top JEE Main Maxima and Minima Questions
- Let the set of all positive values of \( \lambda \), for which the point of local minimum of the function \((1 + x (\lambda^2 - x^2)) \frac{x^2 + x + 2}{x^2 + 5x + 6} < 0\) be \((\alpha, \beta)\).
Then \( \alpha^2 + \beta^2 \) is equal to ________. - If the function \(f(x) = 2x^3 - 9ax^2 + 12a^2x + 1, \, a>0\) has a local maximum at \(x = \alpha\) and a local minimum at \(x = \alpha^2\), then \(\alpha\) and \(\alpha^2\) are the roots of the equation:
- The number of critical points of the function $f(x) = (x - 2)^{2/3}(2x + 1)$ is:
- Let $f(x) = 4\cos^3 x + 3\sqrt{3} \cos^2 x - 10$. The number of points of local maxima of $f$ in interval $(0, 2\pi)$ is:
- Let \( f(x) = 3\sqrt{x - 2} + \sqrt{4 - x} \) be a real-valued function. If \( \alpha \) and \( \beta \) are respectively the minimum and the maximum values of \( f \), then \( \alpha^2 + 2\beta^2 \) is equal to:
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
Concepts Used:
Maxima and Minima
What are Maxima and Minima of a Function?
The extrema of a function are very well known as Maxima and minima. Maxima is the maximum and minima is the minimum value of a function within the given set of ranges.
There are two types of maxima and minima that exist in a function, such as:
- Local Maxima and Minima
- Absolute or Global Maxima and Minima