K Let f(x)=3-x² and let a=-3. Complete parts (a) through (d) below. a. Find the linear approximation L for the function f at the point a L(x)= b. Graph fand L on the same set of axes. Use the graphing tool to graph the functions. Click to enlarge graph 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)=3-x near a=-3 are the graph of t near a d. Compute!'(a) to confirm the conclusion in part (c) The value of f(x) at a = -3 is f'(-3)=, which is confirming the conclusion in part (c) concave because the graph of L 0. This means that fis 10 18 16 12 42 ROO
K Let f(x)=3-x² and let a=-3. Complete parts (a) through (d) below. a. Find the linear approximation L for the function f at the point a L(x)= b. Graph fand L on the same set of axes. Use the graphing tool to graph the functions. Click to enlarge graph 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)=3-x near a=-3 are the graph of t near a d. Compute!'(a) to confirm the conclusion in part (c) The value of f(x) at a = -3 is f'(-3)=, which is confirming the conclusion in part (c) concave because the graph of L 0. This means that fis 10 18 16 12 42 ROO
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:K
Let f(x)=3-x² and let a=-3. Complete parts (a) through (d) below.
a. Find the linear approximation L for the function f at the point a
L(x)=
b. Graph fand L on the same set of axes. Use the graphing tool to graph the functions.
Click to
enlarge
graph
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)=3-x near a=-3 are
the graph of t near a
d. Compute!'(a) to confirm the conclusion in part (c)
The value of f(x) at a = -3 is f'(-3)=, which is
confirming the conclusion in part (c)
concave
because the graph of L
0. This means that fis
10
18
16
12
42
ROO
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