Please explain!

1.)Determine whether the Mean Value theorem can be applied tofon the closed interval[a,b].(Select all that apply.)

f(x) =8x³,[1, 2]

-Yes, the Mean Value Theorem can be applied.

-No, becausefis not continuous on the closed interval[a,b].

-No, becausefis not differentiable in the open interval(a,b).

-None of the above.

If the Mean Value Theorem can be applied, find all values ofcin the open interval(a,b)

such thatf'(c) =f(b)f(a)/ba.(Enter your answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.)

c=?

2.) A rancher has80feet of fencing with which to enclose two adjacent rectangular corrals (see figure). What dimensions should be used so that the enclosed area will be a maximum?

x=?ft

y=?ft

3.) Consider the following function.

f(x) =2x+1/x

(a) Find the critical numbers off. (Enter your answers as a comma-separated list.)

x=?

(b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

increasing= ?

decreasing=?

(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)

relative maximum(x,y)=(?,?)

relative minimum(x,y)=(?,?)

4.)Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)

f(x) =x+5cosx,[0, 2]

(x,y)=?(smallerx-value)

(x,y)=?(largerx-value)

Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

concave upward:?

concave downward:?