Practicing Success
If $f(x)=\sin \left\{\frac{\pi}{3}[x]-x^2\right\}$ for 2 < x < 3 and [x] denotes the greatest integer less than or equal to x, then $f'(\sqrt{\pi / 3})$ is equal to |
$\sqrt{\pi / 3}$ $-\sqrt{\pi / 3}$ $-\sqrt{\pi}$ none of these |
$-\sqrt{\pi / 3}$ |
For 2 < x < 3, we have [x] = 2 ∴ $f(x)=\sin \left(\frac{2 \pi}{3}-x^2\right)$ $\Rightarrow f'(x)=-2 x \cos \left(\frac{2 \pi}{3}-x^2\right)$ $\Rightarrow f'(\sqrt{\pi / 3}=-2 \sqrt{\pi / 3} \cos \pi / 3=-\sqrt{\pi / 3}$ |