List of top Data Science and Artificial Intelligence Questions on Differential Equations asked in GATE AR

Let f: R→ R be a function. Note: R denotes the set of real numbers.
\(f(x) = \left\{ \begin{array}{ll} -x, & \text{if } x < -2 \\ ax^2+bx+c, & \text{if }\ x \in[-2,2]\\ x, & \text{if } x>2 \end{array} \right.\)
Which ONE of the following choices gives the values of a, b, c that make the function f continuous and differentiable ?

Consider the function f: \(\R→ \R\) where \(\R\) is the set of all real numbers.
\(f(x)=\frac{x^4}{4}-\frac{2x^3}{3}-\frac{3x^2}{2}+1\)
Which of the following statements is/are TRUE ?

For any twice differentiable function ƒ: R → R, if at some x* ∈ R, f'(x*) = 0 and f'(x*) > 0, then the function f necessarily has a ______ at x = x*.
Note : R denotes the set of real numbers.