If f(x) = begin{cases} 2a - x & text{when } - | vedclass

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(A) Given,$f(x) = \begin{cases} 2a - x & 	ext{when } -a < x < a \ 3x - 2a & 	ext{when } a \leq x \end{cases}$.First,check for continuity at $x = a$

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$f(x)$ is not differentiable at $x = a$

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(A) Given,$f(x) = \begin{cases} 2a - x & 	ext{when } -a First,check for continuity at $x = a$:Left-hand limit: $\lim_{x 	o a^-} f(x) = \lim_{x 	o a^-} (2a - x) = 2a - a = a$.Right-hand limit: $\lim_{x 	o a^+} f(x) = \lim_{x 	o a^+} (3x - 2a) = 3a - 2a = a$.Value of function: $f(a) = 3(a) - 2a = a$.Since $\lim_{x 	o a^-} f(x) = \lim_{x 	o a^+} f(x) = f(a)$,the function is continuous at $x = a$.Now,check for differentiability at $x = a$:Left-hand derivative: $Lf'(a) = \frac{d}{dx}(2a - x) = -1$.Right-hand derivative: $Rf'(a) = \frac{d}{dx}(3x - 2a) = 3$.Since $Lf'(a) 
eq Rf'(a)$,the function $f(x)$ is not differentiable at $x = a$.

If $f(x) = \begin{cases} 2a - x & \text{when } -a < x < a \\ 3x - 2a & \text{when } a \leq x \end{cases}$,then which of the following is true?

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