Calculus
posted by Nicola on .
Can someone help me finish this question... I got most of the answers but need help.
Suppose that f(x)=3x−6x+5.
(A) Use interval notation to indicate where f(x) is defined. If it is defined on more than one interval, enter the union of all intervals where f(x) is defined.
Domain: (inf,5)U(5,inf)
(B) Find all intercepts. If there are no intercepts, enter None. If there are more than one, enter them separated by commas.
xintercept(s) = 2
yintercept(s) = ?
(C) Find all critical values of f. If there are no critical values, enter None. If there are more than one, enter them separated by commas.
Critical value(s) = none.
(D) Use interval notation to indicate where f(x) is increasing or decreasing. If there are more than one interval, enter the union of all intervals. If the answer is the empty set, enter {}.
Increasing: ?
Decreasing: ?
(E) Find the xcoordinates of all local maxima and minima of f. If there are no local maxima, enter None. If there are more than one, enter them separated by commas.
Local maxima at x = none.
Local minima at x = none.
(F) Use interval notation to indicate where f(x) is concave up or down.
Concave up: ?
Concave down: ?
(G) Find all inflection points of f. If there are no inflection points, enter None. If there are more than one, enter them separated by commas.
Inflection point(s) at x = ?
(H) Find all asymptotes of f. If there are no asymptotes, enter None. If there are more than one, enter them separated by commas.
Horizontal asymptote(s): y = 3
Vertical asymptote(s): x = 5

Assuming you really meant to type
f(x) = 3x^2  6x + 5
then
f'(x) = 6x  6
and
f''(x) = 6
All polynomials are defined for all real values of x.
xintercepts: where f(x) = 0
yintercept: f(x) where x=0
max/min where f'(x) = 0 and f''(x) is not zero
increasing where f'(x) > 0
concave up where f''(x) > 0
inflection where f''(x) = 0
Polynomials have no asymptotes. Rational functions usually have asymptotes
So, having reviewed the information above, what are your answers? We'll be happy to check them for you.