11) (6pts) Suppose that the sales of a particular product given by the function f(x) =...
1. (6pts) Find the domain of f(x) = x+6 V17+ 2x 2. (7pts) Given f(x) = Vx-4, (a) write out the conjugate of f(x+h)-f(x). f(x+h)-f(x) (b) use the conjugate to simplify completely
You can just answer question bcd 5Suppose we have an objective function f(x,y) and a constraint y-h). Suppose the Lagrangian has a critical point at (0,0,X). Explain in a sentence or two how you know that line r(t) = (t,th,(0)) is tangent to the constraint. b At the critical point, compute the second derivative of f along the line in a d2 At the critical point, compute the second derivative of f along the graph y - h(x) Describe the...
36. Revenue Suppose that the revenue function for a certain product is given by R(x) = 15(2x + 1)-1 + 30x – 15 where x is in thousands of units and R is in thousands of dollars. (a) Find the marginal revenue when 2000 units are sold. (b) How is revenue changing when 2000 units are sold?
3. Consider the function f :D → R given by f(x) = the following x - x. With the a (a) Find the derivative of f. Is the function strictly increasing, dec (b) Find the second derivative of f. Is the function strictly concave neither? (c) Suppose D = [0, 1] find the maximum and the minimum of f. (d) Suppose the domain D = (0,1), find the maximum and the min (e) Suppose the domain D = [0, 0),...
11. [-/1 Points] DETAILS SESSCALC2 3.3.037.MI. Suppose the derivative of a function is f'(x) = (x + 1)*(x - 2)(x - 5). On what interval is fincreasing? (Enter your answer in interval notation.)
10. DETAILS HARMATHAPBR1 9.6.001.MI. Differentiate the function. f(x) = (2x - 5)35 F"(x) = 11. DETAILS HARMATHAPBR1 9.9.003. Cost is in dollars and x is the number of units. Find the marginal cost function MC for the given cost function. C(x) = 450 + 16x + x2 MC = 12. DETAILS HARMATHAPBR1 9.9.007. Cost, revenue, and profit are in dollars and x is the number of units. If the total profit function is P(x) = 2x - 15, find the...
QUESTION 18 Suppose you calculate the second derivative of a function to be f(x)-14x-91 and that one critical point? of the critical points is 13. Using the second derivative test, what can you say about the origin al function, f(x), at this O The function has a maximum at 13. The function is increasing for all x < 13. The function has an inflection point at x = 13. O The function has a minimum at 13 O The function...
(Product Rule) Use the Product Rule to find the derivative of the function. f(x) = (4x+5)(x2 -8) O a. 2x + 4 Ob. 12x² + 10x - 32 O c. 8x O d. 8x2 – 40
Verify the product rule for Formal Power Series. Very specifically: Let f(x) be the generating function for a sequence san) and g(x) be the generating function for a sequence sbn1. Using the definitions of multiplication and differentiation of FPS, write down a formula for the derivative of [f(x)g(x)]. Then write down a formula for f(x)g(x) + f(x)g'(x), where f(x) denotes the derivative of f(x). Then show that the two formulas describe the same formal power series. (i.e. both series have...
The revenue function R(x) and the cost function C(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even. R(x) = 200x - 2x2 ; C(x) = - x2 + 5x + 8450 ; 0 ≤ x ≤100 The manufacturer must produce --------------- units to break even.