\(y=f(x)\) is a quadratic function passing through (β1, 0) and tangent to it at (1, 1) is \(y=x\). Find x intercept by normal at point (π, π + 1), (π > 0)
- 7
- -7
- 5
- -5
The Correct Option is A
Solution and Explanation
Top Questions on Application of derivatives
- Consider the following three statements for the function $f : (0,\infty) \rightarrow \mathbb{R}$ defined by
\[ f(x) = \left| \log_e x \right| - |x - 1| : \]
(I) $f$ is differentiable at all $x>0$.
(II) $f$ is increasing in $(0,1)$.
(III) $f$ is decreasing in $(1,\infty)$.
Then,
- JEE Main - 2026
- Mathematics
- Application of derivatives
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.
- CBSE CLASS XII - 2026
- Mathematics
- Application of derivatives
- For $f(x)=x+\dfrac{1}{x}$ $(x\neq0)$
- CBSE CLASS XII - 2026
- Mathematics
- Application of derivatives
- Let \[ f(x)=x^{2025}-x^{2000},\quad x\in[0,1] \] and the minimum value of the function $f(x)$ in the interval $[0,1]$ be \[ (80)^{80}(n)^{-81}. \] Then $n$ is equal to
- JEE Main - 2026
- Mathematics
- Application of derivatives
- Show that the function \( f(x) = 7x^2 - 3 \) is an increasing function when \( x>0 \).
- UP Board XII - 2026
- Mathematics
- Application of derivatives
Questions Asked in JEE Main exam
The correct sequence of reagents for the above conversion of X to Y is :- JEE Main - 2026
- Periodic Table
- If \(x^2+x+1=0\), then the value of \(\left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 + \dots + \left(x^{25} + \frac{1}{x^{25}}\right)^2\) is:
- JEE Main - 2026
- Complex numbers
- Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is ________ cm.
- JEE Main - 2026
- Wave optics
- For some \(\alpha, \beta \in R\), let \(A = \begin{pmatrix} \alpha & 2 \\1 & 2 \end{pmatrix}\) and \(B = \begin{pmatrix} 1 & 1 \\ \beta & 1 \end{pmatrix}\) be such that \(A^2-4A+2I-B^2-3B+I=O\). Then \((\det(\text{adj}(A^3-B^3)))^2\) is equal to:
- JEE Main - 2026
- Matrices and Determinants
MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K.
MX(s) $\rightleftharpoons M^{+(aq) }+ X^{-}(aq)$; $K_{sp} = 10^{-10}$
If the standard reduction potential for $M^{+}(aq) + e^{-} \rightarrow M(s)$ is $(E^{\circ}_{M^{+}/M}) = 0.79$ V, then the value of the standard reduction potential for the metal/metal insoluble salt electrode $E^{\circ}_{X^{-}/MX(s)/M}$ is ____________ mV. (nearest integer)
[Given : $\frac{2.303 RT}{F} = 0.059$ V]- JEE Main - 2026
- Electrochemistry
Concepts Used:
Application of Derivatives
Various Applications of Derivatives-
Rate of Change of Quantities:
If some other quantity βyβ causes some change in a quantity of surely βxβ, in view of the fact that an equation of the form y = f(x) gets consistently pleased, i.e, βyβ is a function of βxβ then the rate of change of βyβ related to βxβ is to be given by
\(\frac{\triangle y}{\triangle x}=\frac{y_2-y_1}{x_2-x_1}\)
This is also known to be as the Average Rate of Change.
Increasing and Decreasing Function:
Consider y = f(x) be a differentiable function (whose derivative exists at all points in the domain) in an interval x = (a,b).
- If for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) β€ f(x2); then the function f(x) is known as increasing in this interval.
- Likewise, if for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) β₯ f(x2); then the function f(x) is known as decreasing in this interval.
- The functions are commonly known as strictly increasing or decreasing functions, given the inequalities are strict: f(x1) < f(x2) for strictly increasing and f(x1) > f(x2) for strictly decreasing.
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