Question

# If $$f(x)=\begin{cases}e^{x}, x< 2\\ a+bx, x\geq 2 \end{cases}$$, is differentiable for all $$x\in R$$ then

A
a+b=0
B
a+2b=e2
C
b=e2
D
none of these

Solution

## The correct options are A $$a+2b=e^{2}$$ C $$b=e^{2}$$ D $$a+b=0$$For given function to be differentiable, it has to be continuous.$$\Rightarrow f(2-)=f(2+)=f(2) => a+2b = e^2$$Also $$f'(2+)=f'(2-)\Rightarrow e^2=b \Rightarrow a=-e^2$$Mathematics

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