f(x) = (4x)/(x^(2)-25) (A) Find all critical values of f . If there are no criti
ID: 2869768 • Letter: F
Question
f(x) = (4x)/(x^(2)-25)
(A) Find all critical values of f. If there are no critical values, enter -1000. If there are more than one, enter them separated by commas.
Critical value(s) =
(B) Use interval notation to indicate where f(x) is increasing.
Increasing:
(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:
(D) Find the x-coordinates of all local maxima of f. If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas.
Local maxima at x =
(E) Find the x-coordinates of all local minima of f. If there are no local minima, enter -1000. If there are more than one, enter them separated by commas.
Local minima at x =
(F) Use interval notation to indicate where f(x) is concave up.
Concave up:
(G) Use interval notation to indicate where f(x) is concave down.
Concave down:
(H) Find all inflection points of f. If there are no inflection points, enter -1000. If there are more than one, enter them separated by commas.
Inflection point(s) at x =
(I) Find all horizontal asymptotes of f. If there are no horizontal asymptotes, enter -1000. If there are more than one, enter them separated by commas.
Horizontal asymptote(s): y =
(J) Find all vertical asymptotes of f. If there are no vertical asymptotes, enter -1000. If there are more than one, enter them separated by commas.
Vertical asymptote(s): x =
Explanation / Answer
1)f(x) = (4x)/(x^(2)-25)
f'(x) = (4(x^(2)-25) -4x*2x)/(x^(2)-25)^2=0
f'(x) = (-4x^(2)-100) -4x*2x)/(x^(2)-25)^2 =0
no critical values
2)increasing f'(x)>0
==>never happerns
3)decreasing
f'(x)<0 always
(-infinity,infinity)
4)no local maxima
5)no local minima
6)concve up(-infinity,0)
7)concve down(0,infinity)
8)(0,0) is inflection point
9)no horizontal asymptote
10)x^2 -25=0==>x=5,x=-5 vertical aymptotes
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.