PHP / SQL UPDATE值WHERE日期等于最大/最新日期

Question

I have a table in Database PhpMyAdmin with certain values, and I want to UPDATE only ONE value of these, WHERE the latest initial_date (TIMESTAMP) is.

I write down here the code I generated as an example, so you can see I actually obtain that date value through SELECT, but I don't manage to UPDATE it. Thank you very much.

$select = "SELECT MAX(initial_date) AS max_value FROM services WHERE matricula = '" . $_POST["taxi"] . "'";
$select_results = mysqli_query($conexion, $select);
while($row = mysqli_fetch_array($select_results)){
    echo $row['max_value'];
    $update_carrera = "UPDATE services SET";
    $update_carrera .= " costo_carrera = costo_carrera + " . $_POST["costo_carrera"] . ",";
    $update_carrera .= " final_date = CURRENT_TIMESTAMP";
    $update_carrera .= " WHERE initial_date = ''";
    $update_carrera_results = mysqli_query($conexion, $update_carrera);
}

I leave WHERE initial_date = '' empty so you can tell what should it be. I get a correct date value in the echo $row['max_value']; if I solve the WHERE with a WHERE initial_date = '20160405153315' (INTEGER), but I don't want to put myself the integer, of course I want to get the newest date from the table database.