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Question
Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?
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Solution
\[f\left( x \right) = ax + b\]
\[f'\left( x \right) = a\]
\[\text { For f(x) to be decreasing, we must have }\]
\[f'\left( x \right) < 0\]
\[ \Rightarrow a < 0\]
\[ \Rightarrow a \in \left( - \infty , 0 \right)\]
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