question_answer 140)

If f(x) = (|x|)3, show that f”(x) exists for all real x and fin it. 

Answer:

. f(x) = (|x|)3                         At x = 0       L.H.D. =                   = 0       R.H.D. =                   Since L.H.D. = R.H.D.                   Now again for       f? (x) = 3x |x|                                     = 3 [|x| + |x|] = 6 |x|       Now for x = 0                f?(x) = 0       To find f? (x) at x = 0                  L.H.D.             R.H.D.             Since L.H.D. = R.H.D.             Hence the result.