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
If \( x = a(0 - \sin \theta) \), \( y = a(1 + \cos \theta) \), find \[ \frac{dy}{dx}. \]
- UP Board XII - 2024
- Mathematics
- Applications of Derivatives
Find the least value of ‘a’ for which the function \( f(x) = x^2 + ax + 1 \) is increasing on the interval \( [1, 2] \).
- UP Board XII - 2024
- Mathematics
- Applications of Derivatives
- The interval in which \(y=x^2e^{-x}\) is increasing is
- CBSE CLASS XII
- Mathematics
- Applications of Derivatives
- The total revenue in Rupees received from the sale of \(x\) units of a product is given by \(R(x)=13x^2+26x+15\).The marginal revenue, when \(x=7\) is
- CBSE CLASS XII
- Mathematics
- Applications of Derivatives
If f (x) = 3x2+15x+5, then the approximate value of f (3.02) is
- CBSE CLASS XII
- Mathematics
- Applications of Derivatives
Questions Asked in CBSE CLASS XII exam
- Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the \( x \)-axis, and the ordinates \( x = -2 \) and \( x = 2 \).
- CBSE CLASS XII - 2025
- Evaluation of Definite Integrals by Substitution
- A 1 cm segment of a wire lying along the x-axis carries a current of 0.5 A along the \( +x \)-direction. A magnetic field \( \mathbf{B} = (0.4 \, \text{mT}) \hat{j} + (0.6 \, \text{mT}) \hat{k} \) is switched on in the region. The force acting on the segment is:
- CBSE CLASS XII - 2025
- Magnetic Effects of Current and Magnetism
The correct IUPAC name of \([ \text{Pt}(\text{NH}_3)_2\text{Cl}_2 ]^{2+} \) is:
- CBSE CLASS XII - 2025
- Coordination Compounds
- Two conductors A and B of the same material have their lengths in the ratio 1:2 and radii in the ratio 2:3. If they are connected in parallel across a battery, the ratio \( \frac{v_A}{v_B} \) of the drift velocities of electrons in them will be:
- CBSE CLASS XII - 2025
- Current electricity
- Arun, Bashir and Joseph were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. They admitted Daksh as a new partner who acquired his share entirely from Arun. If Arun sacrificed \( \frac{1}{5} \)th from his share to Daksh, Daksh's share in the profits of the firm will be :
- CBSE CLASS XII - 2025
- Partnership Accounts
Notes on Applications of Derivatives
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