Question:
Let $a \in R$ and let $f: R \rightarrow R$ be given by $f(x)=x^{5}-5 x+a$, then
Let $a \in R$ and let $f: R \rightarrow R$ be given by $f(x)=x^{5}-5 x+a$, then
Updated On: May 20, 2022
- $f(x)$ has three real roots if $a>4$
- $f(x)$ has only one real roots if $a>4$
- $f(x)$ has three real roots if $a < -4$
- $f(x)$ has three real roots if $-4 < a < 4$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Let $y = x^5- 5x$
Was this answer helpful?
0
0
Top Questions on Maxima and Minima
- Subject to constraints: 2x + 4y ≤ 8, 3x + y ≤ 6, x + y ≤ 4, x, y ≥ 0; The maximum value of Z = 3x + 15y is:
- CUET (UG) - 2024
- Mathematics
- Maxima and Minima
- Let \( f(x) = x^3 - 6x^2 + 12x - 3 \), then at \( x = 2 \), \( f(x) \) has:
- CUET (UG) - 2024
- Mathematics
- Maxima and Minima
- Let the maximum and minimum values of \[\left( \sqrt{8x - x^2 - 12 - 4} \right)^2 + (x - 7)^2, \quad x \in \mathbb{R} \text{ be } M \text{ and } m \text{ respectively}.\] Then \( M^2 - m^2 \) is equal to _____.
- JEE Main - 2024
- Mathematics
- Maxima and Minima
- 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:
- JEE Main - 2024
- Mathematics
- Maxima and Minima
- 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:
- JEE Main - 2024
- Mathematics
- Maxima and Minima
View More Questions
Questions Asked in BITSAT exam
- Minimum value of 5cos(2x) + 5sin(2x)
- BITSAT - 2023
- Trigonometric Functions
- Two capacitors, of capacitance C, are connected in series. If one of them is filled with a dielectric substance K, what is the effective capacitance?
- BITSAT - 2023
- electrostatic potential and capacitance
- What is the dimension of the Gravitational constant?
- BITSAT - 2023
- Gravitation
NaOH is deliquescent
- BITSAT - 2023
- States of matter
- The freezing point of the 0.05 molal solution of non - electrolyte in water is? (kf = 1.86)
- BITSAT - 2023
- Solutions
View More Questions
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