differentiability

Consider the function f(t) = (max(0,t))² for -∞ < t < ∞, where max(a, b) denotes the maximum of a and b. Which of the following statements is/are true?

Consider the function $f(t) = (\text{max}(0,t))^2$ for $- \infty

Let f be a real-valued function of a real variable defined as f(x) = x² for x\ge0, and f(x) = -x² for x<0. Which one of the following statements is true?

A function $f(x)$ is defined as $f(x)=\begin{cases} e^x, & x<1 \ \ln x+ax^2+bx, & x\ge1 \end{cases}$, where $x \in \mathbb{R}$. Which one of the following statements is TRUE?

A function $$f(x)$$ is defined as $$f\left( x \right) = \left\{ {\matrix{ {{e^x},x < 1} \cr {\ln x + a{x^2} + bx,x \ge 1} \cr } \,\,,\,\,} \right.$$ where $$x \in R.$$ Which one of...

Given $$f\left( z \right) = g\left( z \right) + h\left( z \right),$$ where $$f,g,h$$ are complex valued functions of a complex variable $$z.$$ Which ONE of the following statements...