Let f(x)=array|c|c| 3x, & x2 array where [.] denotes greatest integer function.

Question

Let $f(x)=\begin{array}{|c|c|} 3x, & x2 \end{array}$

where [.] denotes greatest integer function. If $\alpha $ and $\beta $ are the number of points, where $f$ is not continuous and is not differentiable, respectively, then $\alpha +\beta $ equals \_\_\_\_\_\_\_ .

Answer: 5

Accepted Answer

$\begin{gathered} f(x)=\begin{gathered} 3x \quad ; \quad x2 \ f(x)=3x \quad ; \quad x2 \end{gathered} \end{gathered}$

Not continuous at $x\in {1,2}\Rightarrow \alpha =2$

Not diff. at $x\in {0,1,2}\Rightarrow \beta =3$

$\alpha +\beta =5$

Solutions · 1