Question

Of the functions below, which will eventually have the greatest rate of change compared to the others? (1 point)

y = 3x + 10



y = x2 + 8x + 1



y = 2x − 3

Answer 1

y = x^2 + 8x + 1.

Reason: the linear functions have constant rates 3 and 2. The quadratic’s instantaneous rate is dy/dx = 2x + 8, which grows without bound as x increases, so for large x it exceeds 3 and 2 (indeed for x > −2.5 it already exceeds 3).