Let x and y be real numbers such that x^2 + y^2 = 1. Find the maximum value of 2x - 5y.

Answer 1

y = +/- sqrt(1-x^2)
if y is to be real, x must be
x^2 </= 1
-1 < x < +1
similarly y ranges from -1 to + 1
so our function 2 x - 5y
is maximum when x is 1 and y is -1
2 + 5 = 7

Answer 2

but, at (1,-1), x^2+y^2 = 2

The maximum occurs when

x = 2/√29
y = -5/√29

Answer 3

Let x and y be real numbers such that x^2 + y^2 = 1. What is the maximum value of 2x - 5y?