Let $f(x)=2+|x|-|x-1|+|x+1|, x \in \mathbf{R}$. Consider $(\mathrm{S} 1): f^{\prime}\left(-\frac{3}{2}\right)+f^{\prime}\left(-\frac{1}{2}\right)+f^{\prime}\left(\frac{1}{2}\right)+f^{\prime}\left(\frac{3}{2}\right)=2$ $(\mathrm{S} 2): \int\limits_{-2}^{2} f(x) \mathrm{d} x=12$ Then,

Question

Let $f(x)=2+|x|-|x-1|+|x+1|, x \in \mathbf{R}$.

Consider

$(\mathrm{S} 1): f^{\prime}\left(-\frac{3}{2}\right)+f^{\prime}\left(-\frac{1}{2}\right)+f^{\prime}\left(\frac{1}{2}\right)+f^{\prime}\left(\frac{3}{2}\right)=2$

$(\mathrm{S} 2): \int\limits_{-2}^{2} f(x) \mathrm{d} x=12$

Then,

both (S1) and (S2) are correct

both (S1) and (S2) are wrong

only (S1) is correct

only (S2) is correct

Solution

Please login to view the detailed solution steps...

Go to DASH