Using calculus, find the coordinates of the stationary point on the curve with equation y = 2x + 3 + \frac{8}{x^2}, x > 0 - Edexcel - A-Level Maths Pure - Question 4 - 2013 - Paper 5

Next, set the derivative equal to zero to find the stationary points:

$2 - 16x^{-3} = 0$

Solving for $x$, we rearrange the equation:

$16x^{-3} = 2$

Multiplying both sides by $x^3$ gives:

$16 = 2x^3$

Dividing by 2 yields:

$x^3 = 8$

Taking the cube root, we find:

$x = 2$

We substitute $x = 2$ back into the original equation to find the corresponding $y$ value:

$y = 2(2) + 3 + \frac{8}{2^2}$

Calculating this, we have:

$y = 4 + 3 + 2 = 9$

Thus, the coordinates of the stationary point on the curve are:

$(2, 9)$