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Let ​f(x)=4−x2and let a=−3. Complete parts​ (a) through​ (d) below.

Let ​f(x)=4−x2and let a=−3. Complete parts​ (a) through​ (d) below.

Calculus: Early Transcendentals
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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Let ​f(x)=4−x2and let a=−3. Complete parts​ (a) through​ (d) below.
 
PARTS A-D ARE THE 1ST IMAGE I INCLUDED BELOW. I kept getting it wrong and those are the questions.
THE SECOND IMAGE IS THE QUESTION. Also please include proper coordinates and correct graph such as the first image shows.
Let f(x) = 4 - x2 and let a = 1. Complete parts (a) through (d) below. a. Find the linear approximation L for the functionfat the point a. L(x) = - 2x + 5 b. Graph f and L on the same set of axes. Use the graphing tool to graph the functions. c. Based on the graphs in part (b), state whether linear approximations to f near a are underestimates or overestimates. Linear approximations to f(x) = 4 -x near a =1 are overestimates because the graph of L lies above the graph of f near d. Compute f''(a) to confirm the conclusion in part (c). The value of f"(x) at a = 1 is f"(1) = -2, which is less than 0. This means that f is concave down, confirming the conclusion in part (c).
Transcribed Image Text:Let f(x) = 4 - x2 and let a = 1. Complete parts (a) through (d) below. a. Find the linear approximation L for the functionfat the point a. L(x) = - 2x + 5 b. Graph f and L on the same set of axes. Use the graphing tool to graph the functions. c. Based on the graphs in part (b), state whether linear approximations to f near a are underestimates or overestimates. Linear approximations to f(x) = 4 -x near a =1 are overestimates because the graph of L lies above the graph of f near d. Compute f''(a) to confirm the conclusion in part (c). The value of f"(x) at a = 1 is f"(1) = -2, which is less than 0. This means that f is concave down, confirming the conclusion in part (c).
Let f(x) = 4 - x2 and let a = 1. Complete parts (a) through (d) below. a. Find the linear approximation L for the functionfat the point a. L(x) = - 2x + 5 b. Graph f and L on the same set of axes. Use the graphing tool to graph the functions. c. Based on the graphs in part (b), state whether linear approximations to f near a are underestimates or overestimates. Linear approximations to f(x) = 4 -x near a =1 are overestimates because the graph of L lies above the graph of f near d. Compute f''(a) to confirm the conclusion in part (c). The value of f"(x) at a = 1 is f"(1) = -2, which is less than 0. This means that f is concave down, confirming the conclusion in part (c).
Transcribed Image Text:Let f(x) = 4 - x2 and let a = 1. Complete parts (a) through (d) below. a. Find the linear approximation L for the functionfat the point a. L(x) = - 2x + 5 b. Graph f and L on the same set of axes. Use the graphing tool to graph the functions. c. Based on the graphs in part (b), state whether linear approximations to f near a are underestimates or overestimates. Linear approximations to f(x) = 4 -x near a =1 are overestimates because the graph of L lies above the graph of f near d. Compute f''(a) to confirm the conclusion in part (c). The value of f"(x) at a = 1 is f"(1) = -2, which is less than 0. This means that f is concave down, confirming the conclusion in part (c).
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