Answer to Question #205381 in Calculus for Akhona Klanisi

Question

13

Given the function f (x) = x⁴ − 2x² + 2,

the second derivative of f is

[a.      −10

[b.   10

[c.   12x² − 4

[d.   2x(x − 5)

Question 14

Customers of a hardware store are willing to buy

Q = 80 − P ²

boxes of nails at P rand per box. Find the marginal revenue if the price per box is R3.

a.       R−53.00

b.       R71.00

c.       R53.00

d.       R−71.00

Answer 1

13.

$f'(x)=4x^3-4x$

$f''(x)=12x^2-4$

Answer: [c].   12x² − 4

14.

Total Revenue:

$TR=QP=80P-P^3=80\sqrt{80-Q}-(80-Q)^{3/2}$

 Marginal revenue:

$MR=\frac{dTR}{dQ}=-40/\sqrt{80-Q}+3\sqrt{80-Q}/2$

For the price R3:

$Q=80-9=71$

$MR=-40/3+9/2=-53/6$