The graph of the derivative f?\' of a continuous function f is shown. (Assume th
ID: 2850224 • Letter: T
Question
The graph of the derivative f?' of a continuous function f is shown.
(Assume the function f is defined only for 0 < x < ?.)
(a) On what interval(s) is f increasing? (Enter your answer using interval notation.)
On what interval(s) is f decreasing? (Enter your answer using interval notation.)
(b) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.)
x =
At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.)
x =
(c) On what interval(s) is f concave upward? (Enter your answer using interval notation.)
On what interval(s) is f concave downward? (Enter your answer using interval notation.)
(d) State the x-coordinate(s) of the point(s) of inflection. (Enter your answers as a comma-separated list.)
x =
(e) Assuming that f(0) = 0, sketch a graph of f. (Do this on paper. Your instructor may ask you to turn in this work.)
y = f'(x) 0 4Explanation / Answer
a) f increasing==>f ' >0
(1,6)U(8, )
f decreasing==>f ' <0
(0,1)U(6,8)
b)for maximum f ' changes from positive to negative. and f ' =0
x=6
for minimum f ' changes from negaitive to positive. and f ' =0
x=1,8
c)concave up ==> (f ')' >0
(0,2)U(3,5)U(7, )
concave down ==> (f ')' <0
(2,3)U(5,7)
d)points of inflectiion ==> (f ')' =0 , (f ')' changes its sign
x=2,3,5,7
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