La funcion que representa el beneficio obtenido por una empresa si vende x unidades de uno de sus productos es f(x)= -70x^2+2800x-45000. ¿cuantas unidades tiene que vender para maximizar sus beneficios?

Let the functions f (x) = x ^ 2-4x + 6andg (x) = 2x-x ^ 2

- (a) Determine, for each of them, the intersection points with the axes, the vertex and the curvature. Represent them graphically

- (b) Determine the value of xfor which the function is minimized h (x) = f (x) - g (x).

(# 3164)      See Solution To select

Calculate the following derivatives:

- (a) f (x) = \ frac {1-3x} {x} + (5x-2) ^ 3

- (b) g (x) = (x ^ 2 + 2) \ cdot Ln (x ^ 2 + 2)

- (c)h (x) = 3 5x + e ^ x

(# 3377)      See Solution To select

The profit obtained by a company, in thousands of euros, is given by the function

f (x) = \ left \ {\ begin {array} {lcr} -5x ^ 2 + 40x-60 & si & 0 \ leq x \ leq 6 \\ \\ \ frac {5x} {2} -15 & if & 6 <x \ leq 10 \\ \ end {array} \ right.  

where x represents advertising spending in thousands of euros.

- a) Represent the function f.

- b) Calculate the advertising expense from which the company has no losses.

- c) For which advertising expenses are there zero profits?

- d) Calculate the advertising spend that produces the maximum profit. What

is that maximum profit?

(# 3380)      See Solution To select

After a test carried out on a new car model, it has been observed that the gasoline consumption c (x), expressed in liters, is given by the function

c (x) = 7.5-0.05x + 0.00025x ^ 2

being x, the speed inkm / h

- a) Determine the gasoline consumption at speeds of 50 km / h and 150 km / h.

- b) Study the growth and decrease of the function c (x).

- c) At what speeds in this interval is the minimum consumption and the maximum consumption obtained and what are these?

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A bank launches an investment plan whose profitability R (x), in thousands of euros, is given according to the amount x, which is invested, also in thousands of euros, by the following expression:,

R (x) = -0.001x ^ 2 + 0.4 x + 3.5with x ≥ 10.

- a) Calculate the profitability for an investment of 100,000 euros.

- b) Deduct and reason how much should be invested to obtain maximum profitability.

- c) What maximum return would be obtained?

Step-by-step explanation: