Deck 27: Differentiation and Integration

Question 1

Find the second derivative () of the equation y = 6x³ + 2x² - 6x + 24

A) = 18x + 4
B) = 18x - 4
C) = 36x - 4
D) = 36x +4

Answer 1

= 36x +4

Question 2

Find the derivative () when y = 2x^-3

A) = -6x^-4
B) = -6x^-3
C) = -6x^-2
D) = 6x³

Answer 2

= -6x^-4

Question 3

Find the integral (∫) of the function 16x³ - 6x² + 4x -3

A) ∫ (16x³ - 6x² + 4x -3) dx = 16x⁴ + 2x³ + 2x² + 3x + C
B) ∫ (16x³ - 6x² + 4x -3) dx = 16x⁴ - 2x³ + 2x² - 3x + C
C) ∫ (16x³ - 6x² + 4x -3) dx = 4x⁴ + 2x³ + 2x² + 3x + C
D) ∫ (16x³ - 6x² + 4x -3) dx = 4x⁴ - 2x³ + 2x² - 3x + C

Answer 3

∫ (16x³ - 6x² + 4x -3) dx = 4x⁴ - 2x³ + 2x² - 3x + C

Question 4

Find the gradient of the equation y = 5x + 25

A) 25
B) 5
C) 1
D) 0.2

Question 5

Which of the following options is the BEST interpretation of the derivative?

A) The value of x which maximised y
B) The value of x which solves the equation
C) The gradient (rate of change) for the equation
D) The mean value of y

Question 6

If y = x⁴ find the derivative ()

A) = x³
B) = 4x
C) = 4x³
D) = 4x⁵

Question 7

Total revenue ( R in €000) for a Italian clothing manufacturer is a function of x (the number of items sold, in hundreds). = 50 - 3x establish the total revenue if 200 items are sold.

A) €92,000
B) €94,000
C) €96,000
D) €98,000

Question 8

A computer component manufacturer in China determines that manufacturing costs (y in Chinese Yuan (CNY)) are determined by an equation y = 0.3x² - 4x +12 (x = quantity manufactured in 100s). Determine the volume of production (x) where costs are minimised (to nearest 10).

A) 660
B) 670
C) 680
D) 690

Question 9

Find the derivative () when y = 8x³

A) = 3x²
B) = 24x³
C) = 5x²
D) = 24x²

Question 10

Find the integral (∫) of the function 4x³

A) ∫ (4x³) dx = x⁴ + C
B) ∫ (4x³) dx = 12x⁴ + C
C) ∫ (4x³) dx = 0.75x⁴ + C
D) ∫ (4x³) dx = 4x⁴ + C