3) The function f(x) = e*(x² + x - 1) has derivatives f'(x) = e* (x2 + 3x), f"(x) = e*(x² + 5x + 3), f"'(x) = e*(x² + 7x+ 8) f has a critical point at x = -3. Is that critical point a local maximum, a local minimum, or neither? (Don't a) forget to justify your answer.)
3) The function f(x) = e*(x² + x - 1) has derivatives f'(x) = e* (x2 + 3x), f"(x) = e*(x² + 5x + 3), f"'(x) = e*(x² + 7x+ 8) f has a critical point at x = -3. Is that critical point a local maximum, a local minimum, or neither? (Don't a) forget to justify your answer.)
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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Question
3a. 3b.
![3) The function f(x) = e*(x² + x – 1) has derivatives
f'(x) = e*(x² + 3x),
f"(x) = e*(x² + 5x + 3), f"(x) = e*(x² + 7x + 8)
f has a critical point at x = -3. Is that critical point a local maximum, a local minimum, or neither? (Don't
forget to justify your answer.)
The function f is continuous on [0, 3]. By the Extreme Value Theorem, f has an absolute minimum on this
b)
interval. Find the x value where it occurs. Explain why the point you found is an absolute minimum.
At x =-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7323f76-5a9c-46b6-9930-86cefe6607d1%2F23d8b5c4-9534-446d-8972-b183d9495fe3%2Fpsk5kwj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3) The function f(x) = e*(x² + x – 1) has derivatives
f'(x) = e*(x² + 3x),
f"(x) = e*(x² + 5x + 3), f"(x) = e*(x² + 7x + 8)
f has a critical point at x = -3. Is that critical point a local maximum, a local minimum, or neither? (Don't
forget to justify your answer.)
The function f is continuous on [0, 3]. By the Extreme Value Theorem, f has an absolute minimum on this
b)
interval. Find the x value where it occurs. Explain why the point you found is an absolute minimum.
At x =-
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