Question

for the function f(x) = 3x-x^3, find:

1) Domain

2) Intercepts (if possible)

3) Intervals of increasing/decreasing and Relative max/min

4) Intervals of concavity and point of inflection

5) End behavior

6) Any vertical and horizontal asymptote

7) Use all the above to make a detailed graph of the function on a grid

please write everything clearly and i'l rate you depending on the work, thanks.

Answer 1

1J 10 10 5 0 10 .-5 -10.

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. Interval Notation: (-00,00)

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in O for x and solve for y. x-intercept(s): (0,0), (V3,0), (-13,0) y-intercept(s): (0,0)

Graph the polynomial in order to determine the intervals over which it is increasing or decreasing Increasing on: (-1,1) Decreasing on: (-0, -1),(1,00)

Find where the first derivative is equal to 0 to find the local maxima and minima. (1, 2) is a local maxima (-1, -2) is a local minima

Use the degree and the leading coefficient to determine the behavior. Rises to the left and falls to the right

Use the inflection points to set up intervals. Substitute a value into each interval to find where the curve is concave up or down. Concave up on (-0,0) since f”(x) is positive Concave down on (0,00) since f”(2) is negative

Since y = 3x – xº is not a rational expression, there are no asymptotes. No Asymptotes