If f(x) array cc x-1 2 x^2-7 x+5 , & for x 1 - 1 3 & , for x=1 array . , then f^ (1) is equal to :

Step-by-step solution

We have, f(x)= x-1 2 x^2-7 x+5 , x 1= (x-1) 2 x^2-2 x-5 x+5 = x-1 2 x(x-1)-5(x-1) = 1 2 x-5 f(x)= array cc 1 2 x-5 , & x 1 - 1 3 , & x=1 array . Now, f^ (1)= _ h 0 f(1+h)-f(1) h = _ h 0 1 2(1+h)-5 - (- 1 3 ) h = _ h 0 1 2 h-3 + 1 3 h = _ h 0 3+2 h-3 3 h(2 h-3) = _ h 0 2 3(2 h-3) =- 2 9