12. The function

\[ f(x) = \begin{cases} 4 - x^2 & \text{if } x \leq 1 \\ mx + b & \text{if } x > 1 \end{cases} \]

is continuous and differentiable for all real numbers. What must be the values of \( m \) and \( b \) ?






Answer is: option4

\( m = -2, \, b = 5 \)

Solution:

.

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