If f(x)= array cc 2 x+3, & x 1 a x^2+b x, & x 1 array . is differentiable x R , then f(2)=

Step-by-step solution

f(x)= array cc 2 x+3, & x 1 a x^2+b x & , x 1 array .f(x) is differentiable x R _ x 1⁻ f^ (x)= _ x 1⁺ f^ (x) 2=2 a+b ... (i) f(x) is continuous x R _ x 1⁺ f(x)=f(1) a+b=5 ... (ii) From (i) and (ii), aligned & a=-3, b=8 & f^ (2)= _ x 2 f(x)-f(x) x-2 & = _ x 2 8 x-3 x^2-4 x-2 = _ x 2 3 x^2-8 x+4 x-2 & =- _ x 2 (x-2)(3 x-2) (x-2) =-4 aligned