Find the values of a and b such that f is continuous and has a derivative at x = 1. Sketch the graph of f.
To sketch: The value of a and b such that the given function is continuous and has a derivative at and to sketch the graph of the given function.
The function is (1)
Apply the condition for continuity of function.
Left hand limit of the given function is,
Right hand limit of the given function is,
From equation (2) and (3).
Apply the condition of differentiability at in equation (1).
The function to be differentiable at , gives .
Substitute 2 for a in equation (4) and get the value of b.
Thus, the value of a and b is 2 and respectively
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