Chapter 10.3, Problem 43E

The length of a rectangle is 4 feet more than 3 times the width. (A = { x w and P = 2l + 2w) (a) Express the area A as a function of the width w. O A = {w square units (2 O A(t) 48 square units 3 3 O A(w) = 3w2 - 4w square units A(w) 4w² + 3w square units O A(w) = 3w2 + 4w square units (b) Express the perimeter P as a function of the length {. O P() =D 을(? - 1) units O P(w) = 8w + 8 units O P(t) = 8l + 8 units O P(t) = -3 8 units O P(t) = 1 units

The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1800 + 12x − 0.1x2 + 0.0005x3 and the company finds that if it sells x yards, it can charge  p(x) = 37 − 0.00021x  dollars per yard for the fabric Use calculus to find the production level for maximum profit. (Round your answer to two decimal places)

Find the linear approximation of f(x)=√x when x = -27. O O G a.) L(x) = -27-3(x-27) b.) L(x) = -3+ (x+27) 27 c.) L(x) = -27+ 12/17 (x+27) d.) L(x) = -3-3(x-27)