Please answer the following questions about the function:
f(x) = 5x^2 / (x^2 - 4)
Instructions:
If you are asked for a function, enter a function.
If you are asked to find x- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None.
If you are asked to find an interval or union of intervals, use interval notation. Enter { } if an interval is empty.
If you are asked to find a limit, enter either a number, I for infinity, -I for -infinity, or DNE if the limit does not exist.
(a) Calculate the first derivative of f. Find the critical numbers of f, where it is increasing and decreasing, and its local extrema.
f'(x) =
Critical numbers x =
Union of the intervals where f(x) is increasing
Union of the intervals where f(x) is decreasing
Local maxima x =
Local minima x =
(b) Find the following left- and right-hand limits at the vertical asymptote x = -2.
lim x->-2- (5x^2 / (x^2 - 4)) =
lim x->-2+ (5x^2 / (x^2 - 4)) =
Find the following left- and right-hand limits at the vertical asymptote x = 2.
lim x->2- (5x^2 / (x^2 - 4)) =
lim x->2+ (5x^2 / (x^2 - 4)) =