The figure below shows f(x) and its local linearization at x = a, y = 4x-4. (The local linearization is shown in blue.) What is the value of a? a = _____ What is the value of f(a)? f(a) = _____ Use the linearization to approximate the value of f(3.2). f(3.2) = _____ Is the approximation an under- or overestimate?

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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The figure below shows f(x) and its local linearization at x = a, y = 4x-4. (The local linearization is shown in blue.)

What is the value of a? 

a = _____

What is the value of f(a)?

f(a) = _____

Use the linearization to approximate the value of f(3.2).

f(3.2) = _____

Is the approximation an under- or overestimate?

The image depicts a graph with two curves plotted on a coordinate plane. 

1. **Axes**: 
   - The horizontal axis (x-axis) is numbered with visible markings at 3 and 6.
   - The vertical axis (y-axis) is not numbered, but both axes have a grid with equal spacing.

2. **Curves**:
   - The **black curve** appears U-shaped, resembling a parabola, and opens upwards. It dips below the x-axis and rises sharply after crossing the vertical line near x = 3.
   - The **blue curve** is a straight line, sloping upwards from left to right, intersecting the x-axis below x = 3 and crossing the black curve at a point between x = 3 and x = 6.

The graph likely represents mathematical functions or equations that are being compared or analyzed for their intersections and behavior over the defined range.
Transcribed Image Text:The image depicts a graph with two curves plotted on a coordinate plane. 1. **Axes**: - The horizontal axis (x-axis) is numbered with visible markings at 3 and 6. - The vertical axis (y-axis) is not numbered, but both axes have a grid with equal spacing. 2. **Curves**: - The **black curve** appears U-shaped, resembling a parabola, and opens upwards. It dips below the x-axis and rises sharply after crossing the vertical line near x = 3. - The **blue curve** is a straight line, sloping upwards from left to right, intersecting the x-axis below x = 3 and crossing the black curve at a point between x = 3 and x = 6. The graph likely represents mathematical functions or equations that are being compared or analyzed for their intersections and behavior over the defined range.
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