How would I go about finding the coordinates minimum point on the curve eg y = e^(x) - 9x -5?

In order to find the coordinates of the minimum point of any curve y = f(x), you must differentiate the equation of the curve with respect to x and then equate it to zero.In this case, the differential of the curve is: dy/dx = e^(x) - 9
Equating this to zero you find that e^x = 9.
Therefore x = ln(9)
Substituting this back int the original equation for the curve to find y: y= e^(ln(9)) - 9ln(9) - 5 , noticing that the e^ ln cancel out.
Thus, x = ln(9) and y = 9-5 - 9ln(9) = 4 - 9ln(9)