\Let f(x) =x^{5} + 5x^{4} + 6x +3. a. Conduct a sign analysi

urca3m403 2021-11-20 Answered
Letf(x)=x5+5x4+6x+3.
a. Conduct a sign analysis of f"". That is, determine the sign off"" on each interval. Make sure to show how you found the boundaries (endpoints) of the intervals and how you computed the sign in each interval.
b. indicate the intervals, if any, on which fis concave up and the intervals, if any, on which fis concave down.
c. Find the x-coordinates of any inflection points of f. If there are more than one, enter them as a comma- separated list. If there are none, enter ""DNE""
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Expert Answer

tnie54
Answered 2021-11-21 Author has 18 answers
Given:
F(x)=x5+5x4+6x+3
differentioting the above ef wet (x) we heve
F1(x)=5x4+20x3+6
again differentiat wet (x),we have
F11(x)=20x3+60x2

(a.) for beundasies (endpoints) of he interval we apply.
F11(x)=0
i.e 20x3+60x2=0
ov, 20x2(x+3)=0
The roots of the abore equation are 0,0 8-3
b) for concave up, F11(x)>0
So,for x3, F(x) is concave up.
(c.) Infection points are those points at which
Function changes its concarity that is concave up to concave down ov vice-versa .
In the secHon(a) ,we see that F11(x) cnange its sign once at -3 where concarity changes from concave down to concave up.
So, the point of Inflection is -3.
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