(1 point) Please answer the following questions about thefunction f(x)=5x2x2?9.

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 alist of numbers separated by commas. If there are no solutions,enter None. If you are asked to find an interval or union ofintervals, use interval notation. Enter { } if an interval isempty. If you are asked to find a limit, enter either a number, Ifor ?, -I for ??, or DNE if the limit does not exist.

(a) Calculate the first derivative of f. Find the criticalnumbers of f, where it is increasing and decreasing, and its localextrema.

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 thevertical asymptote x=?3.

limx??3?5x2x2?9= ? limx??3+5x2x2?9= ?

Find the following left- and right-hand limits at the verticalasymptote x=3.

limx?3?5x2x2?9=? limx?3+5x2x2?9=?

Find the following limits at infinity to determine anyhorizontal asymptotes.

limx???5x2x2?9=? limx?+?5x2x2?9= ?

(c) Calculate the second derivative of f. Find where f isconcave up, concave down, and has inflection points.

f??(x)= __________________________

Union of the intervals where f(x) is concave up___________________

Union of the intervals where f(x) is concave down_____________________

Inflection points x= _______________________

d) The function f is_____ because_____ for all x in the domainof f, and therefore its graph is symmetric about the ________

(e) Answer the following questions about the function f and itsgraph.

The domain of f is the set (in interval notation)______________________________

The range of f is the set (in interval notation) y-interceptx-intercepts _______________________

(f) Sketch a graph of the function f without having a graphingcalculator do it for you. Plot the y-intercept and thex-intercepts, if they are known. Draw dashed lines for horizontaland vertical asymptotes. Plot the points where f has local maxima,local minima, and inflection points. Use what you know from parts(a) - (c) to sketch the remaining parts of the graph of f. Use anysymmetry from part (d) to your advantage. Sketching graphs is animportant skill that takes practice, and you may be asked to do iton quizzes or exams.