Proof of LaGrange's Mean Value theorem

Q. A point on the curve $y=x^2+x$, where the tangent is parallel to the chord joining the points (0, 0) and (1, 2) is .

1. $\left(\frac{1}{2},\frac{3}{4}\right)$
2. $\left(\frac{1}{4},\frac{3}{2}\right)$
3. $\left(\frac{3}{4},\frac{3}{2}\right)$
4. $\left(\frac{1}{2},\frac{5}{4}\right)$

Q. A point on the curve $y=x^2+x$, where the tangent is parallel to the chord joining the points (0, 0) and (1, 2) is .

1. $\left(\frac{1}{2},\frac{3}{4}\right)$
2. $\left(\frac{1}{4},\frac{3}{2}\right)$
3. $\left(\frac{3}{4},\frac{3}{2}\right)$
4. $\left(\frac{1}{2},\frac{5}{4}\right)$