Question:
The set of all values of a for which the function
f(x)=(a²-3a+2)(cos²x-4sin²x/4)+(a-1)x+sin x
does not possess critical points is
The set of all values of a for which the function
f(x)=(a²-3a+2)(cos²x-4sin²x/4)+(a-1)x+sin x
does not possess critical points is
Show Hint
Critical points are obtained from f'(x)=0 or where f'(x) is undefined.
Updated On: Mar 19, 2026
- \([1,\infty)\)
- \((0,1)\cup(1,4)\)
- \((-2,4)\)
- (1,3)∪(3,5)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Critical points occur when f'(x)=0.
Differentiating, the trigonometric part vanishes for all x only when:
a²-3a+2=0 ⟹ a=1,2
Excluding these values gives the interval:
(0,1)∪(1,4)
Was this answer helpful?
0
0
Top Questions on Applications of Derivatives
- Let \( f: \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \( f''(x)>0 \) for all \( x \in \mathbb{R} \) and \( f'(a-1) = 0 \), where \( a \) is a real number. Let \( g(x) = f(\tan^2 x - 2\tan x + a) \), \( 0<x<\frac{\pi}{2} \).
Consider the following two statements :
(I) \( g \) is increasing in \( (0, \frac{\pi}{4}) \)
(II) \( g \) is decreasing in \( (\frac{\pi}{4}, \frac{\pi}{2}) \)
Then,- JEE Main - 2026
- Mathematics
- Applications of Derivatives
- If the volume of a solid hemisphere increases at a uniform rate, prove that its surface area varies inversely as its radius.
- CBSE CLASS XII - 2026
- Mathematics
- Applications of Derivatives
- Find the absolute maximum value of $f(x)=\cos x+\sin^2 x$, where $x\in[0,\pi]$.
- CBSE CLASS XII - 2026
- Mathematics
- Applications of Derivatives
- Find the equation of the tangent to the curve \(y = x^2\) at the point (1,1).
- BITSAT - 2025
- Mathematics
- Applications of Derivatives
- A boat takes 4 hours to travel 40 km downstream and 6 hours to return. The speed of the stream is:
- VITEEE - 2025
- Mathematics
- Applications of Derivatives
View More Questions
Questions Asked in BITSAT exam
- The 5th term of an AP is 20 and the 12th term is 41. Find the first term.
- BITSAT - 2025
- Arithmetic Progression
- A dust particle of mass 4 × 10⁻¹² mg is suspended in air under the influence of an electric field of 50 N/C directed vertically upwards. How many electrons were removed from the neutral dust particle? (g = 10 m/s²)
- BITSAT - 2025
- Electrostatics
- Calculate the electric field at a point due to a uniformly charged spherical shell.
- BITSAT - 2025
- Electrostatics
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Vector Algebra
- Calculate the de Broglie wavelength of an electron moving with a given velocity.
- BITSAT - 2025
- Wave Optics
View More Questions