Calculate the gradients of the tangents to y = x2 at the points given by x = -1 1/2, -1, 1/2, 2 1/2, 7. (Use the gradient function 2x in each case.)

The given x-values are $x = -1\frac{1}{2}$, $-1$, $\frac{1}{2}$, $2\frac{1}{2}$, 7.
In fractional form, these are $x = -\frac{3}{2}$, $-1$, $\frac{1}{2}$, $\frac{5}{2}$, 7.

For $x = -\frac{3}{2}$:

For $x = -1$:

For $x = \frac{1}{2}$:

For $x = \frac{5}{2}$:

For $x = 7$:

The gradients of the tangents at the given points are:
For $x = -1\frac{1}{2}$, the gradient is $\boxed{-3}$.
For $x = -1$, the gradient is $\boxed{-2}$.
For $x = \frac{1}{2}$, the gradient is $\boxed{1}$.
For $x = 2\frac{1}{2}$, the gradient is $\boxed{5}$.
For $x = 7$, the gradient is $\boxed{14}$.