Question

Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R.

Answer 1

f(x) = ax + b

f’(x) = a + 0

f’(x) = a

For, f(x) to be decreasing, it must have

f’(x) < 0

\(\therefore\) a < 0

\(\therefore\) a ∈ (-∞, 0)

Hence the required set of values is a ∈ (-∞, 0).