theory of maxima and minima in differential calculus

In economics, when you plot cost and revenue on the Price-Quantity axis, the profit maximization condition is when marginal cost is equal to marginal revenue. This is a crucial notion to understand. Without it one can't effectively analyze profits. Does this make sense?

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Yes, this is a correct notion. This comes from the theory of maxima and minima in differential calculus which says that the value of a function takes it maximum or minimum value where its first derivative is equal to ...

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The theory of maxima and minima in differential calculus is cited.

Derivatives and graphing; please show all work. See attached.
Pg 176
#24
For the function, f, given in the graph in following figure:
a) sketch f ' (x)
b) Where does f ' (x) change its sign?
c) Where does f ' (x) have local maxima or minima?
#25 Using the answer to previous problem as a guide, write a

For the function of f, given below in graph
(a) Sketch
(b) Where does change its sign
(c) Where does have local minimaandmaxima
Using the graph of write a brief description of complete sentences to describe the relationship between the following features of the function of:
(a) the local maximaandminima o

Show all work
1. Determine the exact value for each of the following limits:
a.
b.
2. Determine derivatives (with respect to x) for the following:
a.
b.
c.
d. Determine for
e. Determine the partial derivative with respect to x for
3. Integrate the following:
a.
b.
c.
4. For the fun

Question 1.
Find the critical points of the function
f(x, y) = 4xy2 - 4x2 - 2y2
and classify them as local maxima, minima or saddles or none of these.
Question 2.
The surface is defined by
z = 3x2 + 2y2 - 3
Find the equation of the tangent plane to the surface at the point (1, 1, 2).
Question 3.
(

Use separation of variables to solve to the ODE:
N ̇=〖{k〗_+-k_- ln〖(N)}N〗;k_+,k_- and t>0;N(0)= N_0>0.
Hint: Use u = ln(N) for u-substitution.
Substitute your solution into the differential equation and show that it is in fact the solution.
Evaluate your solution for N(t) as t→∞ .
For what va

The function has a derivative everywhere and has just one critical point, . In parts (a)-(d), you are given additional conditions. In each case decide whether is a local maximum, a local minimum, or neither. Explain your reasoning. Sketch possible graphs for all four cases.
a)
b)
c)
d)
Please see th

1. f(x)=X3-3X2+5 (-1,3)
I need to find local Maximaand Local Minima for this Question. Also determine where the function is increasing and where it is decreasing. round answer to two decimal places.
2. g(x)= X2+1
(a) Find the average rate of change from -1 to 2.
(b) Find an equation of the secant line containing