If `f(x)=|x-a|phi(x),` where `phi(x)` is continuous function, then (a) `f^(prime)(a^+)=phi(a)` (b) `f^(prime)(a^-)=-phi(a)` (c) `f^(prime)(a^+)=f^(prime)(a^-)` (d) none of these

Answer

Correct options are `(A)` and `(B)`

Explanation

`f(x)=|x-a| \phi(x) \implies f^{\prime}(x)=\frac{|x-a|}{x-a} \phi(x)+|x-a| \phi^{\prime}(x)`


`f^{\prime}(a^{+})=\phi(a), f^{\prime}(a^{-})=-\phi(a)`