Derivative Quiz 4

Find the derivative of f(x) = 3x^2 + 2x - 5

• 3x^3 + 2x^2 - 5x

• 3x^2 + 2x - 5

• 6x + 2

• 9x + 2

Find the derivative of g(x) = sin(x) + cos(x)

• g'(x) = sin(x) - cos(x)

• g'(x) = sin(x) + cos(x)

• g'(x) = cos(x) + sin(x)

• g'(x) = cos(x) - sin(x)

Find the derivative of h(x) = e^x + ln(x)

• h'(x) = e^x - 1/x

• h'(x) = e^x - ln(x)

• h'(x) = e^x + x

• h'(x) = e^x + 1/x

Find the derivative of k(x) = (2x^3 + 5x^2 - 3x + 1)^4

• 4(2x^3 + 5x^2 - 3x + 1)^3(6x^2 + 10x - 3)

• 8x^6 + 20x^5 - 12x^4 + 4

• 16x^9 + 20x^8 - 12x^7 + 4

• 4(2x^3 + 5x^2 - 3x + 1)^2(6x^2 + 10x - 3)^2

Find the derivative of y = (3x^2 + 2x - 5)^3

• 27(3x^2 + 2x - 5)(6x + 2)

• 9(3x^2 + 2x - 5)^2(3x + 2)

• 9(3x^2 + 2x - 5)^3(6x + 2)

• 9(3x^2 + 2x - 5)^2(6x + 2)

Find the derivative of y = sin(2x + 1)

• 2sin(2x + 1)

• sin(2x + 1)

• 2cos(2x + 1)

• cos(2x + 1)

Find the derivative of y = e^(2x^2 + 3x)

• y' = (2e^(2x^2 + 3x))(4x - 3)

• y' = (2e^(2x^2 + 3x))(4x^2 + 3)

• y' = (2e^(2x^2 + 3x))(4x + 3)

• y' = (2e^(2x^2 + 3x))(2x + 3)

A rectangular field is to be enclosed on 3 sides with a fence and on the fourth side with a hedge. If 240 meters of fencing material is available, find the dimensions of the field that will enclose the largest area.

• The dimensions of the field can be found by using the quotient rule of derivatives

• The dimensions of the field can be found by using the integral of the area function

• The dimensions of the field can be found by using the Pythagorean theorem

• The correct answer for the question is the dimensions of the field that will enclose the largest area can be found by solving for x and y using the derivative of the area function.

A manufacturer wants to design an open box with a square base and a volume of 1000 cubic centimeters. Find the dimensions of the box that would minimize the amount of material used.

• The dimensions of the box that would minimize the amount of material used are: x = 10 cm and h = 10 cm

• x = 5 cm and h = 20 cm

• x = 8 cm and h = 12.5 cm

• x = 15 cm and h = 5 cm

A company determines that its profit function is given by P(x) = -2x^3 + 100x^2 - 1000x + 5000. Find the production level that will maximize the company's profit.

• Production level x = 25

• Production level x = 100

• Production level x = 10

• Production level x = 50