business calculus

Question 1

what is the marginal value?

Answer 1

the unit change in the quantity of the independent variable )x) the impact it has on the dependant variable (y or f(x))

Question 2

what is an independent variable?

Answer 2

a variable (often denoted by x ) whose variation does not depend on that of another

eg sales = f(expenditure on advertising)
advertising is the independant variable as it effects sales

Question 3

what is a dependant variable?

Answer 3

Dependent variables depend on other variables. For example, if someone was studying the effects of pollution on asthma, the incidence of asthma would be the dependent variable.

Question 4

can we find the marginal product at points x = 2 and x=7 if p = 20x - x²?

Answer 4

p = 20 (2) - 2² = 36. p = 20 (3) - 3² = 51
51 - 36 = 15 so mp is 15

p - 20 (7) - 7² = 91. p = 20 (8) - 8² - 96
96 - 91 = 5 so mp is 5

this shows that the marginal value of adding one more is greater at x =2 than x = 7 on additional person at 7 gives you less output than it would at 2

Question 5

marginal value slope formula

Answer 5

change in production/ change in labour or dp/ dx

Question 6

whats a tangent line?

Answer 6

touches the specific point without crossing the curve

Question 7

how do you find the marginal value?

Answer 7

draw a tangent to find the values of x and y for each piece of data, eg for x = 7 tangent line would be drawn until x= 0 on one side and to the 8 then youd find the values and use the formula

p2 - p1/ x2-x1

the slop of a tangent at a point approimates the marginal value of a curve at a point

Question 8

what is differentiation?

Answer 8

it allows us to find an expression of a slope without tangents we can put values of x in and find the marginal value

its difference in y/ difference in x

Question 9

what is the slope of the constant function?

Answer 9

0

Question 10

what is the slope of a linear function

Answer 10

y = ax + b whatever the value of a is is the slope of it dy/dx = a

Question 11

how do you do differentiation for a cubic or quadratic formula?

Answer 11

the normal functions are y = ax^3
1. keep a as is
2.multiply a by the power
3. change the power to x^n-1

Question 12

what is the marginal profit?

Answer 12

the profit made from producing another unit

Question 13

how to differentiate for exponential functions…

Answer 13

general form: y = e^ax to differentiate you would do ae^ax

Question 14

how do you differentiate a function that uses ln?

Answer 14

example y = ln (ax) to differntiate would be 1/x

example y = ln (ax + b) = a/ ax+ b so if y = ln(5x + 3) the differentiated it would be 5/ 5x +3