Question 1

What are the critical points of $f\left(x\right)=x^3+6x^2-12$ ?

Accepted Answer

[0,-4]

Answer

[0,-3]

Answer

[0,-2]

Answer

[0,-1]

Question 2

What is the absolute maximum of $f\left(x\right)=x^3+6x^2-12$ ?

Accepted Answer

(-4,20)

Answer

(0,-12)

Answer

(-5,-120)

Answer

(-3,-110)

Question 3

What is the absolute minimum value of $f\left(x\right)=x^3+6x^2-12$ ?

Accepted Answer

(0,-12)

Answer

(-4,20)

Answer

(-5,-120)

Answer

(-3,-110)

Question 4

What is the absolute maximum value of the given graph below?

Accepted Answer

(4,39)

Answer

(1,-14)

Answer

(6,7)

Answer

(0,0)

Question 5

What is the absolute maximum value of $f\left(x\right)=x^3+6x^2-12$ ?

Accepted Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

(-60,0)

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

(0,-60)

Question 6

What is the absolute minimum value of $f\left(x\right)=x^3+6x^2-12$ ?

Accepted Answer

(0,-60)

Answer

(-60,0)

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Question 7

A manufacturer designed a cylindrical can to be produced and it can hold 2liters of liquid. If there is a constraint in materials, what will be the radius of the can that could minimize the amount of materials?

Accepted Answer

r = 6.8278 cm.

Answer

r = 7.8278 cm.

Answer

r = 9.8278 cm.

Answer

r = 8.8278 cm.

Question 8

A manufacturer designed a cylindrical can to be produced and it can hold 2liters of liquid. If there is a constraint in materials, what will be the radius of the can that could minimize the amount of materials?

Accepted Answer

h = 13.6558 cm.

Answer

h = 14.6558 cm.

Answer

h = 12.6558 cm.

Answer

h = 15.6558 cm.

Question 9

A rectangular box has a square base of sides and a volume of 100 cubic centimeters. If the base and top are painted at a cost of 5 cents per square centimeter, and the side with a paint that costs 3 cents per square centimeter, what will be the sides of the base for a minimum cost?

Accepted Answer

3.92 cm.

Answer

6.51 cm.

Answer

4.51 cm.

Answer

5.92 cm.

Question 10

A rectangular box has a square base of sides and a volume of 100 cubic centimeters. If the base and top are painted at a cost of 5 cents per square centimeter, and the side with a paint that costs 3 cents per square centimeter, what will be the height of the base for a minimum cost?

Accepted Answer

6.52 cm.

Answer

3.92 cm.

Answer

4.51 cm.

Answer

5.92 cm.

Question 11

Using Chain Rule, what is the derivative of $f\left(x\right)=x^3+6x^2-12$ ?

Accepted Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Question 12

What is the derivative of $f\left(x\right)=x^3+6x^2-12$ ?

Accepted Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Question 13

Which of the following is the differentiation of $f\left(x\right)=x^3+6x^2-12$ ?

Accepted Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Question 14

What is the derivative of $f\left(x\right)=x^3+6x^2-12$ if chain rule will be applied?

Accepted Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Question 15

Using Chain Rule Differentiation, what is the derivative of $f\left(x\right)=x^3+6x^2-12$ ?

Accepted Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

Answer

$\left(-1,-\frac{119}{2}\right)$

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