For the function F,given by f(x)=x2-6x+8,prove that f '(5)-3f '(2)=f '(8)

Given: f(x)=x^2-6x+8 To Prove : f '(5)-3f '(2)=f '(8) f '(x) is a notation generally used for d(f(x))/dx Therefore f '(x)=d(f(x))/dx=2x-6. [As d(x^m)/DX= mx^(m-1)] Substituting for x, f '(5)=2(5)-6=4 f '(2)=2(2)-6=-2 f '(8)=2(8)-6=10=RHS Now, LHS=f '(5)-3f '(2)= 4 - 3(-2)=4+6=10=RHS Hence Proved.
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