fand g are the functions whose graphs are shown, y = f(x) is in black and y=g(x) in red. Define H(x) = f(x)g(x) and Q(x)=f(g(x)), find the following: a. H'(0) y=g(x)

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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**Transcription for Educational Website**

Given: 

Functions \( f \) and \( g \) are depicted on the graph. The graph for \( y = f(x) \) is shown in black, while \( y = g(x) \) is displayed in red. Define:

\[ H(x) = f(x)g(x) \]
\[ Q(x) = f(g(x)) \]

Find the following:

a. \( H'(0) \)

b. \( Q'(4) \)

**Graph Explanation:**

The graph displays two functions:

- \( y = f(x) \) is a piecewise linear function in black. It appears to increase linearly until \( x = 3 \) and then decreases linearly.

- \( y = g(x) \) is a linear function that is shown in red. It decreases linearly until \( x = 2 \), then increases after \( x = 2 \).

Both functions are plotted on a coordinate plane ranging from \(-2\) to \(6\) on the x-axis and \(-2\) to \(6\) on the y-axis. The intersections and slopes are critical for determining derivatives at specific points as needed in the problems.
Transcribed Image Text:**Transcription for Educational Website** Given: Functions \( f \) and \( g \) are depicted on the graph. The graph for \( y = f(x) \) is shown in black, while \( y = g(x) \) is displayed in red. Define: \[ H(x) = f(x)g(x) \] \[ Q(x) = f(g(x)) \] Find the following: a. \( H'(0) \) b. \( Q'(4) \) **Graph Explanation:** The graph displays two functions: - \( y = f(x) \) is a piecewise linear function in black. It appears to increase linearly until \( x = 3 \) and then decreases linearly. - \( y = g(x) \) is a linear function that is shown in red. It decreases linearly until \( x = 2 \), then increases after \( x = 2 \). Both functions are plotted on a coordinate plane ranging from \(-2\) to \(6\) on the x-axis and \(-2\) to \(6\) on the y-axis. The intersections and slopes are critical for determining derivatives at specific points as needed in the problems.
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