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

Question

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

Swapnal Varma · Answer

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