Write the set of values of a for which the function f(x) = ax + b is decreasing for all xϵR.
f(x) = ax + b
f’(x) = a + 0
f’(x) = a
For, f(x) to be decreasing, it must have
f’(x) < 0
a < 0
a ϵ (-∞, 0)
Hence the required set of values is a ϵ (-∞, 0).
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