problem

Consider the function

F(X) =x²/ x² 4

(a)

Find the domain of f. (Enter your answer using interval notation.)

(b)

Find the intervals on which f is increasing. (Enter your answer as a comma-separated list of intervals.)

Find the intervals on which f is decreasing. (Enter your answer as a comma-separated list of intervals.)

(c)

Find the open intervals on which f is concave up. (Enter your answer as a comma-separated list of intervals.)

Find the open intervals on which f is concave down. (Enter your answer as a comma-separated list of intervals.)

(d)

Find the vertical asymptotes of f.

smaller x-value

x

=larger x-value

x

=

Find the left- and right-handed limits as we approach a vertical asymptote.

As we approach the smaller x-value, the left-handed limit of f is

Select:

or

and the right-handed limit is

---Select---

or

. As we approach the larger x-value, the left-handed limit of f is

---Select---

or

and the right-handed limit is

---Select---

or

.

(e)

Find the horizontal asymptotes of f. (Enter your answers as a comma-separated list of equations.)

(f)

Find the x-intercept.

x =

Find the y-intercept.

y =

(g)

Use the information obtained to sketch the graph of the function.

and

Consider the polynomial functionf(x) =x⁵3x³+ 4x.

(a)

Find the intervals on whichfis increasing. (Hint: Showx= 1

is a critical number. Enter your answer as a comma-separated list of intervals.)

Find the intervals on whichfis decreasing. (Enter your answer as a comma-separated list of intervals.)

(b)

Find the open intervals on whichfis concave up. (Enter your answer as a comma-separated list of intervals.)

Find the open intervals on whichfis concave down. (Enter your answer as a comma-separated list of intervals.)

(c)

Find the local extreme values off. (Round your answers to three decimal places.)

local minimum valuesmaller valuelocal minimum valuelarger valuelocal maximum valuesmaller valuelocal maximum valuelarger value

(d)

Find the global extreme values offon the closed, bounded interval[2, 2].

global minimum valueglobal maximum value

(e)

Find the points of inflection off. (Round your answers to three decimal places.)

smallestx-value(x,f(x)) =

(x,f(x))=

largestx-value(x,f(x))=

and

The position of a particle moving along thex-axis is given byx(t) =t³+9t²21t

witht[0, 2].

(a)

Find the velocity and acceleration of the particle.

velocityv(t)

=accelerationa(t)

=

(b)

For whatt-values is the velocity 0? (Enter your answers as a comma-separated list.)

t=

(c)

When is the particle moving to the left (velocity is negative)? (Enter your answer using interval notation.)

When is the particle moving to the right (velocity is positive)? (Enter your answer using interval notation.)

(d)

What is the farthest the particle gets to the left?

x=

What is the farthest the particle gets to the right?

x=

(e)

When is the velocity increasing? (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

When is the velocity decreasing? (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

(f)

What is the maximum velocity of the particle?

v=