Exams
Subjects
Classes
Home
Exams
Mathematics
Application of derivatives
the least value of a such...
Question:
medium
The least value of \( a \) such that the function \( x^2 + ax + 1 \) is increasing on \([1,2]\) is
Show Hint
For monotonicity on a closed interval, always check the minimum value of the derivative on that interval.
COMEDK UGET - 2025
COMEDK UGET
Updated On:
Apr 28, 2026
4
2
-2
1
Show Solution
The Correct Option is
C
Solution and Explanation
Download Solution in PDF
Was this answer helpful?
0
Top Questions on Application of derivatives
If the function \( f(x) \), defined below, is continuous on the interval \([0,8]\), then:
\[ f(x) = \begin{cases} x^2 + ax + b, & 0 \leq x < 2 \\ 3x + 2, & 2 \leq x \leq 4 \\ 2ax + 5b, & 4 < x \leq 8 \end{cases} \]
BITSAT - 2024
Mathematics
Application of derivatives
View Solution
If
\( x\sqrt{1 + y} + y\sqrt{1 + x} = 0 \),
then find
\( \frac{dy}{dx} \).
BITSAT - 2024
Mathematics
Application of derivatives
View Solution
If \( y = \tan^{-1}\left( \frac{\sqrt{x} - x}{1 + x^{3/2}} \right) \), then \( y'(1) \) is equal to:
BITSAT - 2024
Mathematics
Application of derivatives
View Solution
At \( x = \frac{\pi^2}{4} \), \( \frac{d}{dx} \left( \tan^{-1}(\cos\sqrt{x}) + \sec^{-1}(e^x) \right) = \)
BITSAT - 2024
Mathematics
Application of derivatives
View Solution
Want to practice more? Try solving extra ecology questions today
View All Questions
Questions Asked in COMEDK UGET exam
The solution of \( (x+\log y)dy+ydx=0 \) when \( y(0)=1 \) is
COMEDK UGET - 2025
Differential equations
View Solution
The order of the differential equation \( \frac{d}{dz}\left[\left(\frac{dy}{dz}\right)^3\right]=0 \) is
COMEDK UGET - 2025
Order and Degree of Differential Equation
View Solution
Find the value of \( \displaystyle \lim_{h \to 0} \frac{(a+h)^2 \sin(a+h) - a^2 \sin a}{h} \)
COMEDK UGET - 2025
Derivatives
View Solution
\( 0.2 + 0.22 + 0.022 + \cdots \) up to \( n \) terms is equal to
COMEDK UGET - 2025
Sequence and series
View Solution
The solution set of the system of inequalities \( 5-4x \leq -7 \) or \( 5-4x \geq 7,\ x \in R \) is
COMEDK UGET - 2025
linear inequalities
View Solution