\(y=f(x)\) 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
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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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