It is given that at x = 1, the function x4−62x2+ax+9 attains its maximum value, on the interval [0, 2]. Find the value of a.
It is given that at x = 1, the function x4−62x2+ax+9 attains its maximum value, on the interval [0, 2]. Find the value of a.
Solution and Explanation
Let f(x) = x4−62x2+ax+9.
f'(x)=4x3-124x+a
It is given that function f attains its maximum value on the interval [0, 2] at x = 1.
f'(1)=0
=4-124+a=0
a=120
Hence, the value of a is 120.
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
- 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
- The equation of the tangent to the curve \(y=x^3-2x+1\) at \((1,0)\) is:
- VITEEE - 2025
- Mathematics
- Applications of Derivatives
- A person travels from A to B at 40 km/h and returns at 60 km/h. The average speed for the entire journey is:
- VITEEE - 2025
- Mathematics
- Applications of Derivatives
Questions Asked in CBSE CLASS XII exam
- If $y = a \cos(\log x) + b \sin(\log x)$, then $x^2y'' + xy'1$ is:
- CBSE CLASS XII - 2025
- Continuity and differentiability
A ladder of fixed length \( h \) is to be placed along the wall such that it is free to move along the height of the wall.
Based upon the above information, answer the following questions:(iii) (b) If the foot of the ladder, whose length is 5 m, is being pulled towards the wall such that the rate of decrease of distance \( y \) is \( 2 \, \text{m/s} \), then at what rate is the height on the wall \( x \) increasing when the foot of the ladder is 3 m away from the wall?
- CBSE CLASS XII - 2025
- Application of derivatives
- A meeting will be held only if all three members A, B and C are present. The probability that member A does not turn up is 0.10, member B does not turn up is 0.20 and member C does not turn up is 0.05. The probability of the meeting being cancelled is:
- CBSE CLASS XII - 2025
- Probability
- Vishesh, Manik and Amit were partners in the ratio 5 : 4 : 1. Amit retired on 31st March, 2024. Vishesh and Manik decided to share Amit’s share in the ratio 2 : 3. What will be the new profit sharing ratio between Vishesh and Manik?
- CBSE CLASS XII - 2025
- Retirement and Death of a Partner
- The electric field in a region is given by \( \vec{E} = 40x \hat{i} \, \text{N/C}. \) Find the amount of work done in taking a unit positive charge from a point (0, 3m) to the point (5m, 0).
- CBSE CLASS XII - 2025
- Electrostatics
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