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?
(# 3381) See Solution To select
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: