Suppose f(x) = 4(x - 9)-¹/2. (a) Find f'(x). f'(x) = X X # (b) Find an equation for the line tangent to the graph of f(x) at the point (x, y) = (34, = (34,-) ||
Suppose f(x) = 4(x - 9)-¹/2. (a) Find f'(x). f'(x) = X X # (b) Find an equation for the line tangent to the graph of f(x) at the point (x, y) = (34, = (34,-) ||
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement:**
Suppose \( f(x) = 4(x - 9)^{-1/2} \).
(a) Find \( f'(x) \).
\[ f'(x) = \underline{\hspace{4cm}} \]
(b) Find an equation for the line tangent to the graph of \( f(x) \) at the point \( (x, y) = \left(34, \frac{4}{5}\right) \).
\[ \underline{\hspace{7cm}} \]
**Instructions:**
1. **Differentiation**: Apply the power rule and chain rule to find the derivative \( f'(x) \) for part (a).
2. **Tangent Line Equation**: For part (b), use the point-slope form \( y - y_1 = m(x - x_1) \) where \( m \) is the derivative at \( x = 34 \), and \( (x_1, y_1) = \left(34, \frac{4}{5}\right) \).
There is no graphical representation to explain in this image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe88a8cea-da71-40ab-aaed-a0e0afa0772e%2F45503a4b-4a2d-4c38-9090-d652a2d6c1b7%2F0om67o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Suppose \( f(x) = 4(x - 9)^{-1/2} \).
(a) Find \( f'(x) \).
\[ f'(x) = \underline{\hspace{4cm}} \]
(b) Find an equation for the line tangent to the graph of \( f(x) \) at the point \( (x, y) = \left(34, \frac{4}{5}\right) \).
\[ \underline{\hspace{7cm}} \]
**Instructions:**
1. **Differentiation**: Apply the power rule and chain rule to find the derivative \( f'(x) \) for part (a).
2. **Tangent Line Equation**: For part (b), use the point-slope form \( y - y_1 = m(x - x_1) \) where \( m \) is the derivative at \( x = 34 \), and \( (x_1, y_1) = \left(34, \frac{4}{5}\right) \).
There is no graphical representation to explain in this image.
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