more business calculus - optimization and elasticity Flashcards
what is the turning point?
the max point of the graph and when it begins to downturn
what do you get once the function is differentiated?
the expression of the marginal value
whats the slope at the maximum?
0
whats the slope before the turning point if finding the maximum?
positive
whats the slope after the turning point if finding the maximum?
negative
whats the slope before the turning point if finding the minimum?
negative
whats the slope after the turning point if finding the minimum?
positive
how do you find the marginal value at the turning point?
the turning point is 0 so you make marginal value = to 0 and put it into your formula eg
mv (marginal value) = 50-4x
0=50-4x
50= 4x
50/4=x
x=12.5 which can show the value of the maxium point or the turning point to check its the maximum
you can check the values before to see if theyre positive or negative eg for this example we would look at x =12 and x=13 to see if it is a max or min
how do you find the end points?
use the min and max on range or breakevenpoints
when looking at demand functions where is x?
on the y axis or where quantity is
what is the formula for PED (price elasticity of demand)
p1/ q1 all over difference in price (dp)/ difference in quanitity dx)
how do you find dp/dx
differentitation
when is something inelastic or elastic
inelastic is 0-1 and elastic is above 1
how do you find fixed costs in a function?
fixed costs can be found when x is 0 so whatever is left over is your fixed cost
what is the equation of marginal costs
dc/dx and you differentiate it
