For each of the given functions y = f(x). f(x) = 5, P(2, 1) (a) fınd the slope of the tangent line to its inverse function f ¯1 at the indicated point P. (b) fınd the equation of the tangent line to the graph of f -1 at the indicated point.
For each of the given functions y = f(x). f(x) = 5, P(2, 1) (a) fınd the slope of the tangent line to its inverse function f ¯1 at the indicated point P. (b) fınd the equation of the tangent line to the graph of f -1 at the indicated point.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
![**For each of the given functions \( y = f(x) \).**
\[ f(x) = \frac{4}{1 + x^2}, \quad P(2, 1) \]
(a) Find the slope of the tangent line to its inverse function \( f^{-1} \) at the indicated point \( P \).
(b) Find the equation of the tangent line to the graph of \( f^{-1} \) at the indicated point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffef832d7-febb-470a-ad68-b786ac1e067f%2F19bb122f-ea30-4bf8-a549-dec4e650d781%2Fktft96_processed.png&w=3840&q=75)
Transcribed Image Text:**For each of the given functions \( y = f(x) \).**
\[ f(x) = \frac{4}{1 + x^2}, \quad P(2, 1) \]
(a) Find the slope of the tangent line to its inverse function \( f^{-1} \) at the indicated point \( P \).
(b) Find the equation of the tangent line to the graph of \( f^{-1} \) at the indicated point.
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