Let f(x)=⎧⎪⎪⎨⎪⎪⎩4x2+2[x]x,−12≤x<0ax2−bx,0≤x<12,where [.] denotes the greatest integer function. Then the value of b for which f(x) is differentiable in (−12,12) is:

Let f(x)=⎧⎪⎪⎨⎪⎪⎩4x2+2[x]x,−12≤x<0ax2−bx,0≤x<12,w

1.	Let f(x)=⎧⎪⎪⎨⎪⎪⎩4x2+2[x]x,−12≤x<0ax2−bx,0≤x<12,where [.] denotes the greatest integer function. Then the value of b for which f(x) is differentiable in (−12,12) is:
Answer» Let $f (x) = ⎧ ⎪⎪ ⎨ ⎪⎪ ⎩ \begin{matrix} 4 x^{2} + 2 [x] x, & - \frac{1}{2} \leq x < 0 a x^{2} - b x, & 0 \leq x < \frac{1}{2} \end{matrix},$ where $[.]$ denotes the greatest integer function. Then the value of $b$ for which $f (x)$ is differentiable in $(- \frac{1}{2}, \frac{1}{2})$ is: