Application on differentation Flashcards
What do marginal functions tell us?
tells us how a given function is changing at each point, we can use deratives for this.
Find the exact increase and approximate increase ?
Whats the derative of the cost function, the revenue function and profit function?
What does the first derative test at a point tell us, when f’(x) > 0 and when f’(x)<0, what does this tell us?
tells us whether a function is increasing or decreasing at the point.
When do stationary points occur?
when the first derative is neither increasing or decreasing so f’(x) = 0.
For figure 3a how does the diagram show a maxmium as x increases?
how does figure 3b show a minmium as x increases ?
When finding a max or min, i’e when the first derative is equal to 0, there could be what?
Neither maximum or minimum, there could be a point of inflection
How does this show inflection points as x increases?
What is the notation for the second derative?
What is the second derative of x^3 + x^2 + x? and what is the second derative at the specific point x=2?
What does the second derative test tell us about our function?
Tells us whether our statitonary point is a maximum or a minimum.
IF the second derative test is f’‘(a)<0 then our stationary point is what, if f’‘(a)>0 then our stationary point is what?
if f’‘(a)<0 then our stationary point is a maximum
if f’‘(a) >0 then our stationary point is a minimum.
With the point of inflection what will our second derative test be?
f’‘(a) = 0, however this doesnt tell us whether our stationary point is a point of inflection, we still need to do testing, picking different values and plugging into equation, as it could well be a maxmium as well as a minimum.
1) When we look at e^x, as x goes to infinity what happens to e^x?
2) When we look at e^-x and x goes to infinity what happens to e^x?
What perfect diagram shows e^x as x goes to infinity and e^-x as x goes to infinity?
What are the steps to optimising the function of one variable?
How can we determine whether we have a global maxmin or min or local maximum of min?
We are going to use the first and second derative test
Sketch the curve y =f(x) such that f(x) = x^3-3x^2.
and label if there was a restircted domain x is less than or equal to one and 3., what does this mean?
We have a global minimum at (2,-4)
We have a a global minimum at (0,0)
First of all, find the stationary points and economically meaningful endpoints?
Now draw the diagram and determine the profix max q?
only do 1)
number 1
do iii
do ii
do iv)
