Applied Math question

The price elasticity of demand for a firm’s product is given by

${\eta }_{}$ q / p = − p 25 − 2 p,

where $p$is the price of the firm’s product, in dollars.

Find the firm’s marginal revenue $d$ r / d q ,when the price of its good is $8.00.Find the quadratic Taylor polynomial for the function

A。We don’t have enough information to find the marginal revenue in this case.

B。$\frac{dr}{dq}=8/9.$

C。$\frac{dr}{dq}=-1/8.$

D。

Continuing from the previous problem, if the firm increases their price from $8.00 to $8.40, then the demand for the firm’s product will decrease by . . .

$f$ ( x ) = x 3 ,

centered at the point $x$ 0 = 8.

Show the following work (using the equation editor where necessary):

(i) The derivative and second derivative of the function (you don’t have to show the steps, just the final result).

(ii) The appropriate values of the function and its derivatives, expressed in the form a/b, not as decimals – e.g., 2/3 not 0.666.

(iii) The Taylor polynomial itself.

Consider the function $f$ ( t ) = 4 t 2 e − 0.2 t .

Find the critical point(s) of this function and use the first derivative test to classify its critical value(s) as relative minima, relative maxima or neither.

Use the equation editor to write the derivative and the equation you have to solve to find the critical points.

Comment: You don’t have to write all the math, just the final form of the derivative, etc.

The Savings function for a small nation is given by

$S$ = Y 2 + 5 Y − 30 8 Y + 10.

where S is the nation’s annual consumption (in $billions) and Y is the nation’s annual income (in $billions).

Find the oblique asymptote to the graph of the savings function and interpret your answer in terms of the behavior of the savings function when income grows large.

Comment: Don’t include all the (arithmetic) steps that you took to find the asymptote, but do describe briefly (in words) what you did.