For each function given below, find the open intervals of increase/decrease, all local extreme values, the intervals of concavity, and inflection points.
(a) f(x) = x^2 + 2/x
(b) f(x) = xe^-x

A company is creating a new fertilizer additive for lawn seed, which will be a mixture of nitrogen, phosphate, and potash. Based on their research, the total amount fertilizer added must be at least 14 oz. per 5 lb. bag of lawn seed, but should not exceed 20 oz. per 5 lb. bag. At least ¼ oz. of nitrogen must be used for every ounce of phosphate, and at least 1 oz. of potash must be used for every ounce of nitrogen. The costs per ounce of nitrogen, phosphate, and potash are $0.30, $0.18, and $0.54, respectively. Determine the mixture of the three ingredients in a 5 lb. bag that minimizes costs, as well as that cost.

f(x) = 15x^4-3x^5 / 256. f'(x) = 60x^3 - 15x^4 / 256 f''(x) = 45x^2 - 15x^3 / 64

Find the horizontal and vertical asymptotes

Find the local minimum and maximum points of f(x)

Find all inflection points of f(x)

A rectangular box with no top is to be made to hold a volume of 32 cubic inches. Which of following is the least amount of material used in its construction?

a.) 80 in²

b.) 48 in²

c.) 64 in²

d.) 96 in²

The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one four times as strong as the other, are placed 16 ft apart, how far away from the stronger light source should an object be placed on the line between the two sources so as to receive the least illumination? (Round your answer to two decimal places.)

Solve the differential equation using method of undetermined coefficients.

y'''- 8y = 6xe^2x

1. Assume that a demand equation is given by

q=5000−100p

1. Find the marginal revenue for the production level (value of q) 1000 units

b. The cost of producing q units is given by

C(q)=3000−20q+0.03q2

Find the marginal profit for production level 500 units

A company produces a special new type of TV. The company has fixed costs of ​$476,000 and it costs ​$1300 to produce each TV. The company projects that if it charges a price of ​$2300 for the​ TV, it will be able to sell 750 TVs. If the company wants to sell 800 ​TVs, however, it must lower the price to ​$2000. Assume a linear demand.

What price should the company charge to earn a profit of ​$734,000​?

It would need to charge ​$

Use LHopital rule to solve.

lim (x-1)^(lnx)
x goes to 1+

You need a loan of ​$140 comma 000 to buy a home. Calculate your monthly payments and total closing costs for each choice below. Briefly discuss how you would decide between the two choices. Choice​ 1: 15​-year fixed rate at 7​% with closing costs of ​$1400 and no points. Choice​ 2: 15​-year fixed rate at 6.5​% with closing costs of ​$1400 and 3 points. What is the monthly payment for choice​ 1? ​$ what ​(Do not round until the final answer. Then round to the nearest cent as​ needed

Give an arc-length paramaterization of the line which is the intersection of the tangent planes of z=x^2+y^3 at (1,-1,0) and (1,2,9)

Determine the area inside the first curve but outside the second curve.

r=2sin2θ

r=1

A graphing calculator is recommended.

For the limit

lim x → 2 (x³ − 2x + 4) = 8

illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.)

All vectors are in R^ n. Prove the following statements.

a) v·v=||v||2

b) If ||u||2 + ||v||2 = ||u + v||2, then u and v are orthogonal.

c) (Schwarz inequality) |v · w| ≤ ||v||||w||.