Which of the following functions has the largest value when x = 3?c(x) = 3x2 + 5x + 22j(x) = 12xa(x) = 9x All the functions are equal at x = 3. c(x) j(x) a(x)
Accepted Solution
A:
Answer: c(3) is the largestStep-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 = 7xNow the question is whether c'(3) is larger than j'(3). The latter is ... j'(3) = 7·3 = 21Since 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 = 64j(3) = 12·3 = 36a(3) = 9·3 = 27 c(3) > j(3) > a(3) . . . . . . . c(3) is the largest