Functions Test ...

Let f(x) = ax² + bx + c, where a, b and c are certain constants and a ≠ 0.  It is known that f (5) = −3f(2) and that 3 is a root of f(x) = 0.

What is the other root of f(x) = 0?

Let f(x) = ax² + bx + c, where a, b and c are certain constants and a ≠ 0.  It is known that f (5) = −3f(2) and that 3 is a root of f(x) = 0.

What is the value of a+b+c?

If f (x) = x³ – 4x + p, and f (0) and f(1) are of opposite signs, then which of the following is necessarily true?

Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx², where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.

How many units should Mr. David produce daily ?

Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.

 What is the maximum daily profit, in rupees, that Mr. David can realize from his business?

f1 (x)  = x        0 ≤ x ≤ 1
          = 1        x ≥ 1
          = 0        otherwise

f2 (x) = f1(–x) for all x

f3 (x) = –f2(x) for all x

f4 (x) = f3(–x) for all x

How many of the following products are necessarily zero for every x:

f1(x) f2 (x),          f2 (x) f3 (x),          f2(x) f4 (x)

The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum at