15. A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. Let f be a twice-differentiable function with f (0) = 4. The derivative of f is given by f (z) = sin(22 - 2x + 1) for -2 <¤< 2. %3D (a) Find all values of in the interval -2 < x < 2 at which f has a critical point. Classify each as the location of a relative minimum, a relative maximum, or neither. Justify your answers.
15. A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. Let f be a twice-differentiable function with f (0) = 4. The derivative of f is given by f (z) = sin(22 - 2x + 1) for -2 <¤< 2. %3D (a) Find all values of in the interval -2 < x < 2 at which f has a critical point. Classify each as the location of a relative minimum, a relative maximum, or neither. Justify your answers.
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:15. A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION.
Let f be a twice-differentiable function with f (0) = 4. The derivative of f is given by
f' (x) = sin(x² – 2x + 1) for –2 < ¤ <2.
(a) Find all values of x in the interval -2 < x < 2 at which f has a critical point. Classify each as the
location of a relative minimum, a relative maximum, or neither. Justify your answers.
Please respond on separate paper, following directions from your teacher.
(b) Use the line tangent to the graph of f at x = 0 to approximate f (0.25).
%3D
(c) On the interval 0 <x < 0.25, f' (x) > 0 and f" (x) < 0. Is the approximation found in part (b)
an overestimate or an underestimate for f (0.25) ? Give a reason for your answer.
(d)
-2 <I< 2 cannot equal 1.25.
sing the Mean Value Theorem, explain why the average rate of change of f over the interval
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