Question 1

Find the derivative () when y = 8x3

Accepted Answer

A)  = 3x2 
B)  = 24x3 
C)  = 5x2 
D)  = 24x2 
A)  = 3x2 
B)  = 24x3 
C)  = 5x2 
D)  = 24x2 D

Question 2

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

Accepted Answer

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

Question 3

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).

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Find the integral (∫) of the function 4x3

Accepted Answer

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

Question 6

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.

Accepted Answer

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

Question 7

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

Accepted Answer

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 
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 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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 
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

Question 10

If y = x4 find the derivative ()

Accepted Answer

A)  = x3 
B)  = 4x 
C)  = 4x3 
D)  = 4x5 
A)  = x3 
B)  = 4x 
C)  = 4x3 
D)  = 4x5

Exam 27: Differentiation and Integration

Find the derivative () when y = 8x3

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

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).

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

Find the integral (∫) of the function 4x3

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.

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

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

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

If y = x4 find the derivative ()

Introduction to Business Mathematics and Statistics

Sampling and Data Collection

Data and Their Accuracy

Frequency Distributions and Charts

General Charts and Graphs

Arithmetic Mean

Median

Mode and Other Measures of Location

Measures of Dispersion and Skewness

Standard Deviation

Quantiles and the Quartile Deviation

Linear Functions and Graphs

Regression Techniques

Correlation Techniques

Time Series Model

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Seasonal Variation and Forecasting

Index Relatives

Composite Index Numbers

Special Published Indices

Interest and Depreciation

Present Value and Investment Appraisal

Annuities

Functions and Graphs

Linear Equations

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Cost, Revenue and Profit Functions

Set Theory and Enumeration

Introduction to Probability

Conditional Probability and Expectation

Combinations and Permutations

Binomial and Poisson Distributions

Normal Distribution

Linear Inequalities

Matrices

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Find the derivative () when y = 8x³

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

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).

Find the integral (∫) of the function 4x³

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

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

If y = x⁴ find the derivative ()