6. Decide whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. (12) (a) For continuous function f(x), If f'(c) = 0 and f "(c) > 0, then f(c) is relative minimum. (b) If the graph of f(x) = P(x)/Q(x) has horizontal asymptote, then the degree of the polynomial P(x) must be the same as that of polynomial Q(x). (c) Absolute extrema of a continuous function f always occur at the end points of a closed interval.
6. Decide whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. (12) (a) For continuous function f(x), If f'(c) = 0 and f "(c) > 0, then f(c) is relative minimum. (b) If the graph of f(x) = P(x)/Q(x) has horizontal asymptote, then the degree of the polynomial P(x) must be the same as that of polynomial Q(x). (c) Absolute extrema of a continuous function f always occur at the end points of a closed interval.
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:6. Decide whether the statement is true or false. If it is true, explain why. If it is false, explain
why or give an example that disproves the statement.
(12)
(a) For continuous function f(x), If f'(c) = 0 and f"(c) > 0, then f(c) is relative minimum.
(b) If the graph of f(x) = P(x)/Q(x) has horizontal asymptote, then the degree of the
polynomial P(x) must be the same as that of polynomial Q(x).
(c) Absolute extrema of a continuous function f always occur at the end points of a closed
interval.
(d) If demand is inelastic for a particular value of price x, a small increase in price will
cause a percentage decrease in the quantity sold (demand) that is larger than the percentage
change in price.
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