Question

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 ?

• A. $a=\frac{1}{4},b=0,c=1$
• B. $a=\frac{1}{2},b=0,c=0$
• C. a = 0, b = 0, c = 0
• D. a = 1, b = 1, c = -4

Answer 1

Answer: (A)

$a=\frac{1}{4},b=0,c=1$

Answer 2

The correct option is (A) : $a=\frac{1}{4},b=0,c=1$.