The functions fand g are differentiable for all real numbers, x. The table below gives values of the function and their first derivatives at selected values of x with a being a constant. √g(2x) X 9 1 2 3 4 f(x) 3π 4 8 1 5 f'(x) √2 -6 5 2a² find r'(x) at x = 2. g(x) g'(x) 0 3 4 9 a. If h(x) = sin(f(x)), write the equation of the line tangent to h at x = 1. b. If f(x) = r(x) a -4 1 2 3
The functions fand g are differentiable for all real numbers, x. The table below gives values of the function and their first derivatives at selected values of x with a being a constant. √g(2x) X 9 1 2 3 4 f(x) 3π 4 8 1 5 f'(x) √2 -6 5 2a² find r'(x) at x = 2. g(x) g'(x) 0 3 4 9 a. If h(x) = sin(f(x)), write the equation of the line tangent to h at x = 1. b. If f(x) = r(x) a -4 1 2 3
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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See the attached problem, thank you.
![The functions \( f \) and \( g \) are differentiable for all real numbers, \( x \). The table below gives values of the functions and their first derivatives at selected values of \( x \) with \( a \) being a constant.
\[
\begin{array}{|c|c|c|c|c|}
\hline
x & f(x) & f'(x) & g(x) & g'(x) \\
\hline
1 & \frac{3\pi}{4} & \sqrt{2} & 0 & \frac{1}{a} \\
\hline
2 & 8 & -6 & 3 & -4 \\
\hline
3 & 1 & 5 & 4 & \frac{1}{2} \\
\hline
4 & 5 & 2a^2 & 9 & 3 \\
\hline
\end{array}
\]
**a.** If \( h(x) = \sin(f(x)) \), write the equation of the line tangent to \( h \) at \( x = 1 \).
**b.** If \( f(x) = \frac{1}{\sqrt{g(2x)}} \), find \( r'(x) \) at \( x = 2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6ffa477-99d7-4e93-b7f8-2eced087179b%2F1263ce23-22d3-49b1-b46e-cd578db712d2%2Fpmm863a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The functions \( f \) and \( g \) are differentiable for all real numbers, \( x \). The table below gives values of the functions and their first derivatives at selected values of \( x \) with \( a \) being a constant.
\[
\begin{array}{|c|c|c|c|c|}
\hline
x & f(x) & f'(x) & g(x) & g'(x) \\
\hline
1 & \frac{3\pi}{4} & \sqrt{2} & 0 & \frac{1}{a} \\
\hline
2 & 8 & -6 & 3 & -4 \\
\hline
3 & 1 & 5 & 4 & \frac{1}{2} \\
\hline
4 & 5 & 2a^2 & 9 & 3 \\
\hline
\end{array}
\]
**a.** If \( h(x) = \sin(f(x)) \), write the equation of the line tangent to \( h \) at \( x = 1 \).
**b.** If \( f(x) = \frac{1}{\sqrt{g(2x)}} \), find \( r'(x) \) at \( x = 2 \).
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