Suppose That F(x), F'(x) And F"(x) Are Continuous...

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Suppose that f(x), f'(x) and f"(x) are continuous for real numbersx, and that f has the following properties. i) f is negative on (-∞,6) and positive on (6,∞) ii) f is increasing on (-∞,8) and decreasing on(8,∞) iii) f is concave up on (-∞,3)and concave down on(3,∞) Of the following, which has the smallest numerical value? EXPLAINyour answer. a) f"(3) b) f '(10) c) f '(4) d) f '(1) e) f '(-7)

 

Answer No.1

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A) should be the largest values its where it goes from concaveup to conave down b) - e) you can see from ii) that f is increasing on(-∞,8) and decreasing on (8,∞) (whichbasically means the slope of f or its derivative) from i)f is negative on (-∞,6) and positive on (6,∞),(-∞,6) would have smaller values than (6,∞) with this information get e) to be the answer I hope this helps

Answer No.2

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The answer is (b), because f ' (10) < 0, it has the smallestvalue. It is less than zero because we are told the functionis decreasing for x > 8. The points f ' (4), f ' (1) and f ' (-7) are all positive becausethe function is increasing for x < 8. The value of f '' (3) = 0 since x = 3 is an inflection point. While the above answer is correct, such a function cannot existbecause it is not possible for a function to remain positive forall x > 6 while at the same time be decreasing for x > 8 andbe concave down for all x > 3. The slope is negative andbecoming more negative as x increases.Eventually, the graph of thefunction must cross the x-axis. Tell your instructor, maybe you'llget extra-credit!

Answer No.3

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