If f(x)= array cc a x^2+b x- 13 8 , & x 1 3 x-3, & 1 x 2 b x^3+1, & x 2 array . is differentiable x R , then a-b=

Step-by-step solution

f(x) is differentiable x R f(x) is continuous x R aligned & _ x 2⁺ f(x)= _ x 2⁻ f(x) _ x 2 (6 x^3+1 )= _ x 2 (3 x-3) & 8 b+1=3 b= 1 4 Also, _ x 1⁻ f(x)= _ x 1⁺ f(x) & _ x 1 (a x^2+b x- 13 8 )= _ x 1 (3 x-3) & a+b- 13 8 =0 a+ 1 4 - 13 8 =0 a= 11 8 & a-b= 11 8 - 1 4 = 9 8 aligned