4.The derivative of a function f is given by f'(x)=(-2x-2)e^x, and f(0) = 3. A. The function f has a critical point at x = -1. At this point, does f have a relative minimum, a relative maximum, or neither? Justify your answer. B. On what intervals, if any, is the graph of f both increasing and concave down? Explain your reasoning. C. Find the value of f(-1).
4.The derivative of a function f is given by f'(x)=(-2x-2)e^x, and f(0) = 3. A. The function f has a critical point at x = -1. At this point, does f have a relative minimum, a relative maximum, or neither? Justify your answer. B. On what intervals, if any, is the graph of f both increasing and concave down? Explain your reasoning. C. Find the value of f(-1).
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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4.The derivative of a function f is given by f'(x)=(-2x-2)e^x, and f(0) = 3.
A. The function f has a critical point at x = -1. At this point, does f have a relative minimum, a
B. On what intervals, if any, is the graph of f both increasing and concave down? Explain your reasoning.
C. Find the value of f(-1).
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