Engineering
Mathematics
Basic Rule of Differentiation
Question

Let f and g be two non-zero derivable functions and g' = f 3 and f ' = – g3.  If l is the value of Limx2sgn({x}[x]) and m = f4(2)+g4(2)f4(0)+g4(0) then find the value of (l + m).

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Solution

let    h (x) = g4(x) + f 4(x)
        h'(x) = 4g3g' + 4f 3 f ' = 4 f 3 g3 – 4 f 3 g3 = 0
    h(x) = constant
    m = 1
and    =Limx2sgn({x}[x])=1
  l + m = 2