Which of the following functions has the largest value when x = 3? c(x) = 3x2 + 5x + 22 j(x) = 12x a(x) = 9x all the functions are equal at x = 3. c(x) j(x) a(x)

  c(3) is the largest

Step-by-step explanation:

For positive values of x, j(x) > a(x), so the comparison is between c(x) and j(x).

Without evaluating the functions, you can subtract 5x from them to get ...

  c'(x) = c(x) -5x = 3x² +22

  j'(x) = j(x) -5x = 7x

Now the question is whether c'(3) is larger than j'(3). The latter is ...

  j'(3) = 7·3 = 21

Since c'(3) has an added constant of 22 and x² will be positive, we know that ...

  c(3) > j(3) > a(3)

The function with the largest value at x=3 is c(x).

You can, of course, simply evaluate the functions:

  c(3) > j(3) > a(3) . . . . . . . c(3) is the largest

 d) 6   e) 10     g) 900

Step-by-step explanation:

d)

98² = 9604

9610 - 9604 = 6

e)

54² = 2916

2916 - 2906 = 10

g)              10            12          15

                 ∧             ∧            ∧

               2·5         2·2·3       3·5

The Perfect square is: 2² · 5² · 3² = 30²

30² = 900