Question

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

Answer 1

$$\begin{gathered} f\left(x\right)=ax+b \\ f\text{'}\left(x\right)=a \\ \text{For}\mathit{\text{f}}\text{(}\mathit{\text{x}}\text{) to be decreasing, we must have} \\ f\text{'}\left(x\right)<0 \\ \Rightarrow a<0 \\ \Rightarrow a\in \left(-\infty ,0\right) \end{gathered}$$