The gravitational potential energy of the MIR space station, in joules, at a distance of x kilometers from the centre of the Earth, is described by the equation

$\displaystyle E = -\frac{(5.38)(10)^{19}}{x}$. Determine the slope of the tangent to the graph at the given value of x.

$\displaystyle x = (6.5)(10)^6 m$

My answer:

$\displaystyle x = (6.5)(10)^6 m = 6500 km$

$\displaystyle m = \frac{E(6500 + 0.001) - E(6500)}{0.001}$

$\displaystyle m = \frac{(-\frac{(5.38)(10)^{19}}{(6500 + 0.001)}) -(-\frac{(5.38)(10)^{19}}{(6500)})}{0.001}$

$\displaystyle m = 1.273(10)^{12}$

Is this correct?