Question

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)

Answer 1

It’s D

Explanation:

a(x)

Answer 2

c(3) is the largest

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) = (3·3 +5)·3 +22 = 14·3 +22 = 42 +22 = 64
• j(3) = 12·3 = 36
• a(3) = 9·3 = 27

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