Q3

Let $f$ be a function defined by

$$f(x)=\begin{cases} x^2 & \text{for } x \le 1 \\ ax^2 + bx + c & \text{for } 1 &lt x \le 2\\ x + d & \text{for } x > 2 \end{cases}$$

Find the values for the constants $a, b, c$ and $d$ so that $f$ is continuous and differentiable everywhere on the real line.