# Quiz 27: Differentiation and Integration

Business

Free

Multiple Choice

C

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Multiple Choice

D

Free

Multiple Choice

A

Q 4Q 4

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

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Multiple Choice

Free

Multiple Choice

Q 6Q 6

Find the second derivative () of the equation y = 6x

^{3}+ 2x^{2 }- 6x + 24 A) = 18x + 4 B) = 18x - 4 C) = 36x - 4 D) = 36x +4Free

Multiple Choice

Q 7Q 7

A computer component manufacturer in China determines that manufacturing costs (y in Chinese Yuan (CNY)) are determined by an equation y = 0.3x

^{2}- 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) 690Free

Multiple Choice

Q 8Q 8

Find the integral (∫) of the function 4x

^{3}A) ∫ (4x^{3}) dx = x^{4}+ C B) ∫ (4x^{3}) dx = 12x^{4}+ C C) ∫ (4x^{3}) dx = 0.75x^{4}+ C D) ∫ (4x^{3}) dx = 4x^{4}+ CFree

Multiple Choice

Q 9Q 9

Find the integral (∫) of the function 16x

^{3 }- 6x^{2 }+ 4x -3 A) ∫ (16x^{3 }- 6x^{2 }+ 4x -3) dx = 16x^{4}+ 2x^{3}+ 2x^{2}+ 3x + C B) ∫ (16x^{3 }- 6x^{2 }+ 4x -3) dx = 16x^{4}- 2x^{3}+ 2x^{2}- 3x + C C) ∫ (16x^{3 }- 6x^{2 }+ 4x -3) dx = 4x^{4}+ 2x^{3}+ 2x^{2}+ 3x + C D) ∫ (16x^{3 }- 6x^{2 }+ 4x -3) dx = 4x^{4}- 2x^{3}+ 2x^{2}- 3x + CFree

Multiple Choice

Q 10Q 10

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

Free

Multiple Choice