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Differential Calculus | Differentiability

Consider the following statements in respect of the function y = [x], x ∈ (-1, 1) where [.] is the greatest integer function: 1. Its derivative is 0 at x = 0.5 2. It is continuous at x = 0 Which of the above statements is/are correct?
Let g(x) = f(x) + f(2+x), where  \( f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1 - \left| x \right|,\;\;\left| x \right| \le 1}\\ {0,\;\;\left| x \right| > 1} \end{array}} \right.\) The number of points where the function g is not differentiable is
Consider the following statements: 1. The function f(x) = | x | is not differentiable at x = 1 2. The function f(x) = ex is differentiable at x = 0. Which of the above statements is/are correct?
The intervals for which the function f(x) = -2x3 + 3x2 + 12x + 25 is increasing is:
The intervals for which the function f(x) = - 2x3 + 3x2 + 12x + 25 is increasing is:
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