# Calculus and statistics

*label*Mathematics

*timer*Asked: Jun 17th, 2018

*account_balance_wallet*$10

**Question description**

Please see attached file.

Please show all of your work in order to receive full credit. If you are making use of a particular property

or theorem, be sure to state/show that the hypotheses are satised. It would be greatly appreciated to complete this in 24 hours.

## Tutor Answer

Attached.

Question 1.

For the function f (x) = x3 + 3x2,

find the following:

(a) Horizontal or vertical asymptotes, if any.

Solution.

Horizontal asymptote.

A line y=K would be the horizontal asymptote of the above function if;

The lim (x3+3x2) =k

x-α

or if f(x)=k where k is a finite number

x-α

hence on calculating the limits

⁘The lim (x3+3x2) =

x-α

limx3=∞

and

lim 3x2 =3lim x2 + ∞ Where ∞=constant

the

x→∞

x→∞

thus, the lim of the equation =∞

thus, there is no Horizontal asymptote

Vertical asymptote.

A line y=K would be the vertical asymptote of the above function if;

The lim (x3+3x2) =∞

x-α

where the denominator is 0

however, the function has no 0 denominator thus there is no vertical asymptote.

(b) Points of maximum and minimum and the value of the function at these points.

Solution.

The maximum point of a function f (x) = x3 + 3x2 should satisfy the ...

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